Open Access The Design of the Acoustic Isolator Used in Acoustic Telemetry While Drilling. Xie Haiming 1,2*, Zhou Jing 2 and Zhang Feng 3

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1 Send Orders for eprints to The Open Petroeum Engineering Journa, 015, 8, Open Access The Design of the Acoustic Isoator Used in Acoustic Teemetry Whie Driing Xie Haiming 1,*, Zhou Jing and Zhang eng 3 1 Xidian University, Xian, , P.. China; Xian Shiyou University, Xian, , P.. China; 3 China Ship Scientific esearch Center, Xian, , P.. China Abstract: The acoustic isoator between the driing bit and the acoustic piezoeectric transducer can attenuate the driing noise transmitted through the dri coar to avoid interference with the transmission of acoustic signas whie driing, and aso can be used to weaken the infuence of downink acoustic signa with the upink channe produced by the transducer. This paper improves the characteristic anaysis of tapered acoustic transmission mode, and the size and structure of the acoustic isoator has been designed which has the characteristic frequencies of 700~800Hz and 100~1300Hz. Keywords: Acoustic isoator, Acoustic teemetry whie driing, Acoustic transmission, Modeing anaysis. 1. INTODUCTION The wireess Measurement Whie Driing system (MWD) is widey used in the fied of driing, can rea-time detect and upoad the formation parameters and borehoe attitude parameters in the driing process to ensure that the borehoe trajectory is driing in accordance with the requirements. The transmission medium of MWD can be mud puse and eectromagnetic waves, acoustic and optica fiber etc. The MWD of mud puse or eectromagnetic waves has been widey used in oified. Affected by the driing fuid, the method of mud puse MWD cannot be used in air driing or foam driing, and the transmission capacity is imited. The domestic instrument s transmission rate can ony reach 3-5bps, but it can reach 10bps in other countries. The method of eectromagnetic waves MWD cannot be used in the ow resistivity formation, and the transmission distance is imited, which can not be appied to the deep we operation [1-4]. The acoustic teemetry whie driing technique uses eastic waves for data transmission in the dri coumn, cannot be infuenced by driing fuid and formation resistivity. With the infuence of dri strings cyce section and driing noise, the theoretica rate of acoustic transmission can reach 100bps [1]. In 007, XACT downhoe teemetry company pubished the transmission rate of downhoe acoustic transmission system to 0bps, and the test we depth is 500m [5, 6]. Compared with the acoustic information transmission system used in production wes, the entire system is the first to be affected by the noise in the process of driing and the wave refected by the dri assemby under the teemetry system. These kinds of noise are transmitted into the acoustic transmission channe, which causes interference with the *Address correspondence to this author at the Xidian University, Xian, Shaani, , P.. China; Te: ; a: ; E-mai: haimingie@syu.edu.cn acoustic teemetry signa. The downhoe BHA cannot be designed according to the characteristics of acoustic teemetry transmission system. Therefore the acoustic isoator must be designed to eiminate acoustic refection noise [1]. The acoustic teemetry instruments whie driing are mainy composed of acoustic transmitting transducer, receiving transducer, acoustic isoator and the supporting eectronic circuit components. The Acoustic signas generated by acoustic transmitting transducer propagates upward aong the dri pipe to the surface, and a refection signa is generated when the acoustic signa propagates down to the downhoe dri assemby, which interferes with the upink signa seriousy. The acoustic isoator is positioned between the driing bit and the transmitting transducer. The acoustic isoator has two major functions: attenuating the driing noise through the acoustic isoator above the driing bit to avoid the noise signa propagating aong the dri coar and affecting the acoustic signa teemetry; weakening the infuence of the refection signa produced by transmitting transducer for the upink channe. In the acoustic teemetry signa transmission process whie driing, the noise generated by the dri bit is mainy in the frequency band range beow 600Hz. The transmitting band of signa is seected from 700Hz to 000Hz [7-10]. This paper mainy competes the design of acoustic isoator with transmission channe frequency of 700~800Hz and 100~1300Hz interva.. THE CEATION O A TANSMISSION MODE The cacuation methods for acoustic transmission in the periodic dri pipe mainy incude Dougas finite difference method and the equivaent transmission fim method [11]. The former can ony cacuate the acoustic transmission characteristics of periodic dri pipe with two kinds of cross / Bentham Open

2 48 The Open Petroeum Engineering Journa, 015, Voume 8 Haiming et a. section, the atter can aso cacuate the sound transmission characteristics of various cyindrica section combined pipe structure, but not for the tapered section rod and various specia-shaped rods. The design of an acoustic isoator is mainy dependent on finite eement software and the test of mode after machining. There is no fast estimation method that can be used in practica engineering [1-0]. According to the characteristics of the structure design of the acoustic isoator, the four-poe network parameter transfer matri for the vibration of different cross section cyindrica bars or tapered bars, is obtained based on the structure ongitudina vibration theory. The vibration transmission characteristics of the acoustic isoator with arbitrary cross section combined structures has been got under certain boundary conditions. According to the input and transfer impedance of the acoustic isoator, the reationship between the vibration speed and the force of the input and output at the two ends of the acoustic isoator has been obtained. Thus the mode design method of the acoustic isoator engineering cacuation has been competed..1. The Estabishment of Various Tapered Cyindrica Pipe Vibration Equation and the our End Parameter Equation 1. The vibration equation of inear tapered cross section pipe ig. (1). Linear tapered cross section pipe vibration dispacement reationship. The vibration dispacement reationship of variabe crosssection cyindrica rod is shown in ig.(1). The foowing assumptions are made: A partices in the rod ony have the aia dispacement, and each partice is ony the function of coordinates and time; The strain in the pipe is uniformy distributed over the entire cross section, and the cross section has no bending deformation; If the ongitudina stress is appied to the section position, its dispacement is!, then the dispacement at the position of + d is! + d!, which d! is the incrementa dispacement; The strain and stress in the pipe: a ξ ξ + d 1 s( ) d + The strain rate is the ratio of unit ength dispacement increment and unit ength, "!!" % # $! & d d!"! The ongitudina stress T is the compression force on the per unit area of the cross section T s( ), is the cross-sectiona area of the pipe at position. Among them: c Y! is the ongitudina wave veocity and s in the materia. Considering the simpe harmonic vibration of the structure!!e j"t, Then it can be obtained:!!! + 1!s s!!!! + k! 0 (1) Among them: k! c is the ongitudina wave number. The equation (1) is the dispacement equation of one dimensiona ongitudina vibration of the variabe section bar. The veocity of the simpe harmonic vibration can be written in the form of v!!!t j"!e j"t. If the vibration dispacement in the pipe is the independent variabe of ais and timet, the equation (1) can be written in the form of differentia equations of partice vibration veocity:!! v! + 1!s!v s! + k v 0 () The transfer force of the pipe is: ξ Ys Ys( ) j ω v ) Soving the equation is divided into two types: 1. uniform cross-section cyindrica pipe;.variabe cross-section uniform cyindrica pipe. (1) Uniform cyindrica pipe with equa section 0 0 ig. (). Uniform cyindrica pipe of equa section. As shown in ig. (), if z!cs 0, the above equations can be soved to get the reationship between input and output, which can be written in the form of the four-poe parameters matri: (3)

3 The Design of the Acoustic Isoator Used in Acoustic Teemetry Whie Driing The Open Petroeum Engineering Journa, 015, Voume v cos sin 1 k k v jz 1 jz sin k cos k The eements in the matri formua (4) are four-poe parameters for uniform cyindrica pipe vibration. They describe the reationship between the vibration transfer veocity and the eastic force of the input and output at both ends of a cyindrica rod. () Variabe cross-section uniform cyindrica pipe If the pipe is a variabe cross-section coumn, the cross sectiona area s( ) is a function of position coordinates, then soving the equation is more compe. Then the vibration equations of severa variabe cross-section cyindrica bars can be soved to get the four-poe parameters equations. 1. Linear tapered cross section pipe As shown in ig. (1), the cross-sectiona area of a inear tapered cross section pipe can be epressed as shown beow: π 1 s r π + 1 The reation between input and output can be obtained by soving the above equations (3) and (5): v v v Among them: fg g f fg gf 1 fg g f jz fg gf fg fg jz1 fg g f z f g g f z fg gf The four-poe network parameters reation of a tapered rod is written as a matri form: v v. The equa wa thickness hoow tapered pipe At each end of the driing pipe, there is a wa thick hoow tapered rod with a thread, as shown in ig. (3). d 1 ig. (3). The equa wa thickness hoow tapered pipe. d out out1 in in1 0 (4) (5) (6) (7) Through the soution, the foowing four-poe parameters matri formua can be obtained: v v Among them: g f f g fg fg 1 fg fg jz fg fg g f f g jz1 fg fg z f g g f z fg fg 3. The hoow straight tapered pipe d1 ig. (4). The hoow straight tapered pipe. (8) (9) (10) (11) (1) As shown in ig. (4), the epression of the soution is the same as of the Linear straight tapered pipe. Assuming 0 or respectivey, the epressions of veocity and eastic force at both ends of the rod are obtained. After simpification, the four-poe parameters matri equation of the hoow straight tapered pipe can be obtained: v1 γ11 γ1 v γ γ b 1 1 (13) Among them, the four-poe parameters! 11,! 1,! 1,! are the same as of the parameters! 11,! 1,! 1,! of the inear tapered pipes, but the height of the conica tip is changed from a to b. With tapered bore cyindrica pipe 0 r 0 0

4 430 The Open Petroeum Engineering Journa, 015, Voume 8 Haiming et a. ig. (5). With tapered bore cyindrica pipe. The femae thread connecting the dri pipes is usuay a straight cyindrica rod with a conica hoe. The structure profie is shown in ig. (5), the radius of the outer cyindrica pipe is, the sma end radius of the inside hoow conica pipe is 1, the other end radius is, the ength is. The four-poe parameters matri structure of input and output can be got: v1 χ11 χ1 v χ χ among them: f χ11 g f k f k ( )( sin cos ) 1 1 g sin k χ 1 g ( ) 3 1 ( ) z Df 1 k 1 f1 1 χ k g χ ( ) ( ) jz Dsin k k cos k g k g (14) (15) (16) (17) (18) f g cos k+ g ksin k (19) f g sin k g kcos k (0) 1 1 jz g3 g( f1sin k fcos k) (1) k.. The our-poe Parameters of the Tapered Pipe with a everse Structure When the structure is positivey ecited, the cacuation methods of four-poe parameters of the ongitudina vibration transmission characteristics have been given in the above sections. But in fact, the structure can be aso subjected to reverse impact ecitation or paced in the opposite direction under the reverse ecitation, so that the inverse matri of the four end parameter matri of the structure needs to be soved. Then the inverse four-poe parameters matri of the structure can be obtained. The matri of the four-poe parameters of the forward transfer of the structure is as foows: 0 v1 a11 a1 v a a () If the structure is under reverse incentives, the matri of the four-poe parameters can be written as foows: v b11 b1 v1 b b 1 1 (3) The two transfer matrices satisfy the foowing reation: b11 b1 a11 a1 b b a a THE DESIGN O THE ACOUSTIC ISOLATO (4) 3.1. The Design of the Variabe Cross Section Acoustic Isoator According to the standard of dri pipe, ig. (6) iustrates the structure of the acoustic isoator which has been designed. The output end of the structure is on the eft, whie the input end is on the right. At both ends of acoustic isoator is the NC50 standard thread joint. The ength of each side is different. The ength of the eft joint structure is 54mm, the radius is 89mm, and the ength of the right joint structure is 9.1mm, and the radius is 89mm. The hoow straight cone pipe is used to connect the joint structure with the centra cyindrica pipe. The ength of the eft straight cone pipe is 80mm, and the ength of the eft straight cone pipe is 70mm. The ength of the midde sma section cyinder pipe is 345.4mm and the section radius is 63.5mm. The ength of the arger section of cyinder pipe is 1500mm, whereas the section radius is 89mm. The whoe ength of the acoustic isoator is mm, and the maimum section radius is 89mm. The acoustic isoator body is divided into 7 sections of hoow cyindrica rod and conica rod with different cross sections to be simuated. Based on the structura vibration theory, the vibration transmission characteristics of the structure are obtained by putting the structure parameters of each section into the cacuation program. The resuts are shown in igs. (7, 8). The combined structure of the threaded joints of two dri rods is a cyindrica structure with equa cross section. Therefore, the NC50 threaded joint can be considered as an equa section cyinder for simuation. ig. (6). The design of cyindrica pipes combining acoustic isoator. ig. (7) iustrates the transfer coefficient of the veocity and ecitation force of an acoustic isoator under different boundary conditions. rom the cacuated vaues of the ordinates, the maimum vaue is 9.85e3, the minimum vaue is 0.177, the variation range is between 0.1 and 10000, and it is over 5 orders of magnitude. The phenomenon of enargement is obvious, and there is obvious phenomenon of signa

5 The Design of the Acoustic Isoator Used in Acoustic Teemetry Whie Driing The Open Petroeum Engineering Journa, 015, Voume ampification. ig. (8) shows the veocity admittance curve of the structures input force under the free boundary condition, and it is aways the speed response of the output end with the input force of 1N. The maimum veocity occurs at the 30Hz, the vaue is 0.053m/s. The corresponding frequency points of the other peak vibration points are: 451Hz 93Hz 1051Hz 1505Hz 1735Hz 1974Hz 439Hz etc. ig. (10). Through cacuation, the natura frequency of the structure is obtained as shown in Tabe 1, the natura mode of the structure is obtained as shown in ig. (11), and the transfer response curve of the structure under the ecitation of the unit force is aso presented. transmission coefficien t 输 (v/v1) 输 (/1) ig. (7). The transfer coefficient with the output end free and fied boundary conditions. transmission mobiity (Ns/m) ig. (8). The transfer admittance curve with the condition of the output end free. ig. (9) shows the structure transfer admittance curve with the frequency band of Hz. The stop bands of the acoustic isoator are designed in Hz and Hz. As shown in ig. (9), there is no resonance peak in the two frequency bands. The vaues of the transfer admittance are reduced to 0.3% and 0.09% of the resonance peak, that is compared with resonance peaks of 93Hz and 1051Hz, which are reduced by 49.7dB and 61.dB. transmission mobiity (Ns/m) frequency (Hz) frequency (Hz) 输 (v/1) 输 (v/1) frequency (Hz) ig. (9). The structura transfer admittance curve of the frequency band. 3.. The inite Eement Simuation of the Variabe Crosssection Acoustic Isoator In order to verify the design, the finite eement software ANSYS is used to simuate the design mode as shown in ig. (10). The finite eement mode of the acoustic isoator. Tabe 1. Order The natura frequency of the acoustic isoators first 8 orders. Simuation vaue Theoretica vaue Error % In Tabe 1, the error of the natura frequency between the cacuated resuts and the theoretica anaysis is not more than 3.%, and the minimum difference between the frequencies is 10Hz. rom the natura moda anaysis of the structure, it can be seen that the vibration dispacement at both ends of the acoustic isoator is the argest at the resonance frequency. The unit ecitation force is appied to the upper end of the acoustic isoator to cacuate the vibration transmission characteristics of structure under free boundary condition, to acquire the node vibration veocity of the acoustic isoators ower end. The resut of finite eement simuation of structura transfer admittance is compared with that of theoretica cacuation, as shown in ig. (1). The differences between the cacuation resuts of the structura transfer admittances finite eement simuation are compared with the resuts of theoretica cacuations, as shown in ig. (1). The peak frequency of finite eement cacuation is consistent with the theoretica cacuation resuts before 3000Hz.

6 43 The Open Petroeum Engineering Journa, 015, Voume 8 Haiming et a. ig. (11). The natura mode of the acoustic isoators first si order modes. Veocity Mobiity (m/sn) 论计 值 仿 值 requency (Hz) ig. (1). The comparison of theoretica cacuation with finite eement simuation of the acoustic isoators speed transfer admittance. The damping factor is considered in the finite eement harmonic response anaysis, but the structura damping is not considered in the theoretica cacuation. Therefore, the cacuated vaue of the finite eement is sighty smaer than the theoretica vaue on the peak vaue. The pass band and stop band of the finite eement cacuation frequency are fuy consistent with the theoretica cacuation vaues, which aso proves the reiabiity of this cacuation method again. CONCLUSION Through the anaysis of the ongitudina vibration transfer reationship of a variabe cross-section cyindrica rod, the epressions of ongitudina vibration speed and force acting on input and output terminas of the variabe crosssection cyindrica or conica rods are obtained, the four-poe parameters characterization method for acoustic vibration transmission of dri string is estabished. Through comparison, it is shown that the defined transfer admittance parameter can refect the vibration transfer characteristics of combined dri string structure. By comparison, it can be shown that the defined parameters of transfer admittance can refect the vibration transmission characteristics of the combined dri string structure. Based on this method, the structure of acoustic isoator composed of variabe cross-section cyindrica rods is designed, the theoretica cacuation of which is

7 The Design of the Acoustic Isoator Used in Acoustic Teemetry Whie Driing The Open Petroeum Engineering Journa, 015, Voume consistent with the finite eement simuation resuts. The transmission characteristics of the acoustic isoator body meet the design requirements of the sound attenuation of 50dB in the Hz or the Hz bands. CONLICT O INTEEST The authors confirm that this artice content has no confict of interest. ACKNOWLEDGEMENTS Decared none. EEENCES [1] L. Chao, The esearch and Deveopment of MWD Data Acoustic Transmission Technoogy Based on Dri Pipe, PhD thesis, China University of Petroeum, 010. [] C. Litian, The esearch of Acoustic Sending and eceiving Eectronic System Aong Dri Strings, PhD thesis, China University of Petroeum, 011. [3] M. Zhe, Y. Jinzhou, and Z. Jinhai, The appication situation and deveopment trend of wireess MWD Technoogy, Petroeum Driing Techniques, vo. 35, no. 6, pp , 007. [4] T. Bing, MWD Mud Puse Signa Identification and Ground Adaptation Technoogy esearch, PhD thesis, Beijing University of Technoogy, 013. [5] L. Cheng, J. Zhongwu, and L. Zhao, Modeing and simuation anaysis for an acoustic isoation structure in a dristring channe, Journa of Vibration and Shock, vo. 3, no., pp , 67, 013. [6] D. Zhifeng, The Structure Design of MWD Acoustic Teemetry System of Oi and Gas Wes, PhD thesis, China University of Petroeum, 011. [7] T. Xiaoming, S. Yuanda, and T. Baohai, Dri-foowing Acoustic Logging Method and Device Capabe of educing and Insuating Sound on Dri Coar, China, CN [P] [8] S. Xue, esearch on Measurement and Anaysis of Dristring Vibration, PhD thesis, China University of Petroeum, 010. [9] Y. Wei, Signa Detection of the Dri Bit Seismic Wave Whie Driing, Institute of Geophysics, China Earthquake Administration, 007. [10] Z. Xueqin, The Dynamics Anaysis of od String in Screw Pump We end esearch Eccentric Wear Prevention Methods, Daqing Petroeum Institute, 010. [11] D. S. Drumheer, Acoustica properties of dri strings, Journa of Acoustica Society of America, vo. 85, no. 3, pp , [1] L. Cremer, Structure-Borne Sound, Springer-Verag Berin Heideberg, 005. [13]. ahy, Sound and Structura Vibration, Esevier, 007. [14] N. Jianhua, esearch on Piezoeectric Transducer Consistency Screening Technoogy and Sound Isoator Design Technique, PhD thesis, Tianjin University, 009. [15] Y. Xianghong, S Yuanda, and S. Jianmeng, Acoustic characteristics of aisymmetric periodic groove structures, Chinese Journa of Computationa Physics, vo. 7, no. 6, pp. 8-89, 010. [16] Z. Chuni, Numerica Simuation and Eperiments on Isoator Logging-Whie-Driing (LWD) Acoustic Too, PhD thesis, China University of Petroeum, 011. [17] Z. Meiing, Numerica Simuation Investigation on Sound Isoator of Acoustic Logging Whie Driing, PhD thesis, China University of Petroeum, 011. [18] S. Yuanda, Z. Chuni, D. Line, L. Yuia, and Q. Yukun, Eperimenta esearch on Performance Evauation of LWD Acoustic Isoator, We Logging Technoogy, vo. 35, no. 5, pp , 011. [19] W. Guoping, Patent anaysis for the acoustic ogging whie driing technoogy, Petroeum Instruments, vo. 4, no. 3, pp. 1-3, 010. [0] L. Bin, W. ang, C. Dehua, and C. Chenguan, Numerica simuation on acoustic insuation performance of a periodic nonaisymmetry groove structure, Appied Acoustics, vo. 31, no. 5, pp , 01. eceived: May 6, 015 evised: Juy 14, 015 Accepted: August 10, 015 Haiming et a.; Licensee Bentham Open. This is an open access artice icensed under the terms of the ( which permits unrestricted, noncommercia use, distribution and reproduction in any medium, provided the work is propery cited.