Numerical modeling of DPSK pressure signals and their transmission characteristics in mud channels

Transcription

1 66 Pet.Si.(9)6:66-7 DOI.7/s Numerial modeling of DPSK pressure signals and their transmission harateristis in mud hannels Shen Yue, Su Yinao, Li Gensheng 3, Li Lin and Tian Shoueng 3 College of Physis Siene and Tehnology, China University of Petroleum, Dongying, Shandong 576, China CNPC Drilling Researh Institute, Beijing 83, China 3 State Key Laboratory of Petroleum Resoures and Prospeting, China University of Petroleum, Beijing 49, China Abstrat: A numerial model and transmission harateristi analysis of DPSK (differential phase shift keying) pressure signals in mud hannels is introdued. With the ontrol logi analysis of the rotary valve mud telemetry, a logial ontrol signal is built from a Gate funtion sequene aording to the binary symbols of transmitted data and a phase-shift funtion is obtained by integrating the logial ontrol signal. A mathematial model of the DPSK pressure signal is built based on priniples of ommuniations by modulating arrier phase with the phase-shift funtion and a numerial simulation of the pressure wave is implemented with the mathematial model by MATLAB programming. Considering drillpipe pressure and drilling fluid temperature profile along drillpipes, the drillpipe of a vertial well is divided into a number of setions. With water-based drilling fluids, the impats of travel distane, arrier frequeny, drillpipe size, and drilling fluids on the signal transmission were studied by signal transmission harateristi analysis for all the setions. Numerial alulation results indiate that the influenes of the visosity of drilling fluids and volume fration of gas in drilling fluids on the DPSK signal transmission are more notable than the others and the signal will distort in waveform with differential attenuations of the signal frequent omponent. Key words: Measurement while drilling (MWD), modulation, binary symbol, mathematial model, numerial simulation, differential phase shift keying (DPSK), signal transmission harateristis Introdution In modern drilling, measurement while drilling (MWD) and logging while drilling (LWD) provide effetive means for monitoring drilling and formation parameters during drilling, whih improves drilling effiieny and drilling safety. Mudpulse telemetry is urrently the most ommon method of MWD and LWD. Data from the downhole MWD tool is transmitted to the surfae via a pressure wave generated in the mud olumn inside the drillpipe and the pressure wave is deteted at the surfae standpipe using a pressure transduer and then sent a signal proessing unit for deoding, reording, and interpretation (Monroe, 99; Wasserman et al, 8). The growing demand for more real-time downhole information needs high data transmission rates, espeially with the development of geosteering and lose-loop drilling tehnology (Lesso and Chau, ; Zhang, 3; Li et al, 7). Early MWD mud telemetry systems generated pressure pulse in mud hannels by using a plunger valve and transmitted downhole data with a baseband transmission pattern (Grosso et al, 983), so the data rate was slow and at approximately 3 bps. Now the baseband transmission pattern has been replaed by frequeny-band transmission pattern * Corresponding author. suyinao@petrohina.om.n Reeived September, 8 with a ontinuous pressure wave mud telemetry system of relatively higher data rate up to bps and better tolerane of normal noise soure (Klotz et al, 8). Generally, frequenyband transmission of downhole measurements uses the data modulation sheme of differential phase shift keying (DPSK) or quadrature phase shift keying (QPSK) (Hutin et al, ). Some studies have been onduted to analyze the influene of baseband signal frequeny and drilling fluid harateristis on downhole signal transmission (Liu and Su, ; Shmalhorst et al, ; Shi and Liu, ). Beause of differential signal harateristis and frequeny spetrum distribution between baseband and frequeny-band signals, there are differential transmission influenes on them in mud hannels. This paper introdues a method of modeling DPSK pressure signals by mathematial analysis of the logial ontrol signals of rotary valve mud telemetry and priniple of ommuniations. Considering the influene of pressure and temperature profile along the well depth on signal transmission, numerial omputation is used to analyze the signal transmission harateristis along the entire length of a vertial well. Mathematial model of DPSK pressure signals The proess of enoding data onto the mud pressure wave is known as modulation. The downhole measurements

2 Pet.Si.(9)6: are onverted to enoded binary words onsisting of binary bit and by an A/D (analog to digit) onverter and enoder. The frequeny band transmission of enoded data an be implemented by modulating the arrier phase with a digital baseband signal, alled DPSK modulation. In DPSK modulation, the digital baseband signal is omposed of bit periods as a standard unit and eah bit period generally onsists of several arrier yles. In the first arrier yle of eah bit period, a binary bit is transmitted by slowing the rotor speed of a rotary valve to produe a 8 degrees lag in the sine arrier phase and a binary bit is transmitted by keeping the original moving state of the rotary valve. When an enoded logial pulse sequene L(t), the pulse width being limited to a arrier yle T, is applied on the motor ontroller of the rotary valve a DPSK pressure signal is produed. Aording to ommuniation priniples (Jiang et al, 7), a DPSK pressure signal an be expressed as: () t A sin[ t f()] t DPSK where A is the arrier amplitude, Pa; ω is the angular frequeny of the arrier wave, rad/s, T ; T is the arrier period, s, T ; f is the arrier frequeny, Hz; t is time, f s; θ is the initial phase of the arrier wave, degrees; f(t) is phase-shift funtion. Considering the ondition of single logial pulse L (t) modulation, if phase-shift funtion is f (t) and θ =, the modulated signal an be expressed as: t Asin t T A sin[ t f ( t)] Asin( t) t T DPSK By analyzing the equation above, f (t) and L (t) an be formulated as follows: f () t T t t L ()dt t T t T t T () () With Fourier transform and inverse Fourier transform of f (t), we an get the phase-shift funtion: T T () sin[ ( t )]d T f t As an example in a formation resistivity phase DPSK signal generated by PowerPulse MWD ontinuous wave telemetry system, Shlumberger (Martin et al, 994), eah bit period is omposed of four arrier yles and the data is transmitted in the sheme of bits binary symbol, so the logial pulse ode an be defined as: C a a a a a a a a a a where α n (n =,, ) is a binary symbol of phase modulation logi, α n = denotes phase modulating while α n = denotes no phase modulating. When the binary symbols transmit from α to α in sequene an enoded logial pulse sequene L(t) is built and eah symbol ours in the time intervals of 4T, this is equivalent to being a 4(n )T time lag related to the first pulse, then a logial pulse sequene funtion an be built as follows: L() t a L () t a L ( t4 T ) a L ( t36 T ) alt [ 4( n) T] n n where L (t) is the single pulse modulation funtion, () ( T L ) t G t ; G(t) is the unit Gate funtion. Therefore we an get the phase-shift funtion: t f() t L()d t t T T 7T an sin[ ( t 4 nt )]d n T (4) Substituting Eq. (4) into Eq. (), a DPSK pressure signal mathematial model with bits binary symbol an be built as follows: (3) T 7T DPSK () t A sint an sin[ ( t 4 nt )]d n T (5) 3 Transmission harateristi analysis of pressure signals in mud hannels In drillpipes filled with drilling fluids, the transmission of pressure wave deays in an exponential way with travel distane (Hutin et al, ). x px ( ) ps exp( ) S (6) with d Kl S Kd l Kl Kl f [ g( ) s( )] Ee Kg Ks (7) e e ( ) ( )( ) e/ d d d where p(x) is the pressure wave amplitude at distane x, Pa;

3 68 Pet.Si.(9)6:66-7 p s is the pressure wave amplitude at signal soure, Pa; S is the attenuation index of pressure wave amplitude, m; d is the internal diameter of the drillpipe, m; f is signal frequeny, Hz; μ is the kinemati visosity of drilling fluids, Pa s; K l is the bulk modulus of liquid in drilling fluids, Pa; K g is the bulk modulus of gas in drilling fluids, Pa; K s is the bulk modulus of solids in drilling fluids, Pa; β g is the volume fration of gas in drilling fluids, %; β s is the volume fration of solids in drilling fluids, %; E is the bulk modulus of the drillpipe, Pa; e is the wall thikness of the drillpipe, m; δ is the Poisson s ratio of the drillpipe. The bulk modulus of gas and volume fration of gas in drilling fluids are related to drillpipe pressure and drilling fluid temperature. In the ase of a vertial well, the drillpipe is divided into N setions. When N is big enough, the pressure and temperature of eah setion ould be regarded as invariable. Then the pressure attenuation index in the ith setion of mud hannel an be determined as: d Si Kl Kd l p (73 Ti ) Kl Kl f [ g ( ) ( )] s Ee Di Di Ks [ pm ( Di ) ](73 T) m[ pm ( Di ) ] dg dg where m is the speifi heat ratio of gas (m=.); p is the wellhead pressure, Pa; β g is the wellhead volume fration of gas in drilling fluids, %; T i is the temperature at the position i of the well, C; T is the wellhead temperature, C; p m is the wellhead pump pressure, Pa; T i is the well depth, m; λ is the flow frition resistane fator; v is the average flow veloity of drilling fluids, v=4q/(πd ), m/s; Q is the drilling fluid flow rate, m 3 /s; ρ is the drilling fluid density, kg/m 3 ; g is the gravitational aeleration, m/s. Signals reeived at the surfae are the result of soure signal transmitting from bottom-hole passing N setions of mud hannels: p N x i p exp ( ) i Si s where x i is the length of the ith setion of mud hannel, m, D xi N ; D is the true vertial depth, m; N is the divided setion number of true vertial depth. 4 Numerial simulation and analysis of DPSK pressure signals Suppose that the drilling fluid is water-based, the omputational onditions are as follows (Liu and Su, ). The internal diameter of drillpipe was 8.6 mm, drillpipe wall thikness was 9. mm; drillpipe Poisson s ratio was.3, drillpipe bulk modulus was. 5 MPa, volume fration of gas in drilling fluids was.5%, volume fration of solids in drilling fluid was 5%, bulk modulus of solids in drilling fluid was.68 4 MPa, bulk modulus of liquid in drilling fluid was.4 3 MPa, drilling fluid kinemati visosity was mpa s, drilling fluid flow rate was 3 L/s, true vertial depth was 3, m, wellhead pump pressure was MPa, wellhead mud temperature was 4 degrees entigrade and bottom-hole temperature was 9 degrees entigrade, mud temperature linearly inreased from wellhead to bottom-hole in the drillpipe. The drillpipe was divided into, setions and the logial pulse ode was. 4. Numerial simulation and waveform analysis Based on the DPSK signal mathematial model (Eq. (8) (5)), in the onditions of A C =, f = Hz, and θ=, results of numerial simulation for signal waveform and transmission with a distane of, to 3, m are shown in Fig.. Simulation results show that the DPSK soure signal generated by the mathematial model orresponds to the rule of the arrier wave being modulated by the binary symbol. Beause of signal energy loss in the transmission proess, the signal amplitude gradually attenuates and distorts in waveform with transmission distane. Attenuations in high frequeny omponents of the signal are relatively higher than the low frequeny omponents. This illustrates that the mud hannel ats as a low-pass filter with variable parameters and its gain gradually attenuates with the travel distane. The filter parameters are related to well depth, drillpipe size, drilling fluid visosity, and volume fration of gas in drilling fluids aording to Eq. (8).. Soure signal -..5 m m 3m Time, s Fig. Simulated DPSK pressure signal waveform and transmitted results with distane 4. Numerial analysis of signal transmission harateristis in mud hannels Signal transmission harateristis are related to travel distane, drillpipe size, arrier frequeny, and drilling fluids. Considering the transfer funtion of the signal transmission hannel being defined as signal amplitude ratio, under influene of the arrier frequeny, drillpipe internal diameter,

4 Pet.Si.(9)6: drilling fluid visosity and volume fration of gas in drilling fluids, the numerial results of the amplitude ratio with travel distane are shown in Figs. -5. Numerial results indiate that the signal amplitude deays in an exponential way with travel distane, and influenes of both drilling fluid visosity and volume fration of gas in drilling fluids are more notable than the others.. d=8.6mm, μ=mpa s, g =.5% d=8.6mm, f =Hz, g =.5% μ=mpa s μ=4mpa s μ=6mpa s μ=8mpa s.8 f =Hz f =Hz..6.4 f =5Hz f =Hz f =5Hz 3 Travel distane, m Fig. 5 Influene of the visosity of drilling fluids on signal transmission. 3 Travel distane, m Fig. Influene of arrier frequeny on signal transmission d=8.6mm, f =Hz, μ=mpa s 3 Travel distane, m Fig. 3 Influene of the volume fration of gas in drilling fluids on signal transmission f =Hz, μ=mpa s, g =.5% Travel distane, m g = g =.5% g =.% g =.5% g =.% d=88.6mm d=98.6mm d=8.6mm d=8.6mm 3 Fig. 4 Influene of the internal diameter of drillpipe on signal transmission Influene of wellbore and signal parameters on signal transmission an be explained as follows. ) The drilling fluid pressure signal an be regarded as drilling fluid partiles moving in a mehanial osillation, whih ould make elasti media partiles transfer mehanial energy and ause pressure waves to propagate in drillpipe. When osillating partiles overome the resistane from the pipe wall and adjaent partiles, there is energy loss, resulting in great signal attenuation when drilling fluid visosity inreases and the internal diameter of drillpipe dereases. Beause the partile osillating veloity is related to osillating amplitude and frequeny, larger amplitude and higher frequeny make larger osillating veloity, whih aounts for that signal attenuation being greater near signal soure than those far away from it, leading to non-linearity in exponential of deay of signal amplitude ratio with the distane. ) The influene of volume fration of gas in drilling fluids is mainly aused by sattering loss produed by gasliquid interfae diffuse refletion when pressure waves meet disrete phase gas in drilling fluids. 5 Conlusions ) A model of the DPSK pressure signal is based on the mathemati analysis of enoded logial pulse sequene of the rotary valve. ) DPSK transmissions in mud an produe waveform distortion as well as amplitude attenuation, beause attenuations in high frequeny omponents of signal are higher than in low frequeny omponents. 3) Numerial analysis indiates that the influene of drilling fluid visosity and volume fration of gas in drilling fluids on DPSK pressure signal transmission are more notable than other fators at the same travel distane. 4) Beause of the influene of the internal diameter of drillpipe on DPSK pressure signal transmission, there ould be larger signal energy loss in the proess of slim-hole drilling and oiled tubing drilling. Aknowledgements This work was finanially supported by High Tehnology

5 7 Pet.Si.(9)6:66-7 Researh and Development Program of China (No. 6AA6A). The authors would like to express their thanks for the approval to publish this paper. Referenes Gro sso D S, Rader D and Ryanal J C. Report on MWD experimental downhole sensors. Journal of Petroleum Tehnology (5): (SPE paper 58) Hutin R, Tennet R W and Kashikar S V. New mud pulse telemetry tehniques for deepwater appliations and improved real-time data apabilities. SPE/IADC Drilling Conferene held in Amsterdam, The Netherlands, 7 Febuary- Marh, (SPE paper 6776) Jia ng L, Wu H H, Yan S Q, et al. Priniples of ommuniations. Beijing: Tinghua University Press (in Klo tz C, Bond P, Wasserman I, et al. A new mud pulse telemetry system for enhaned MWD/LWD Appliations. IADC/SPE Drilling Conferene held in Orlando, Florida, 4-6 Marh, 8 (SPE paper 683) Klo tz C, Wasserman I and Hahn D. Highly flexible mud-pulse telemetry: a new system. Indian Oil and Gas Tehnial Conferene and Exhibition held in Mumbai, India, 4-6 Marh, 8 (SPE paper 358) Lesso W G and Chau M. Continuous diretion and inlination measurements revolutionize real-time diretional drilling deisionmaking. SPE/IADC Drilling Conferene held in Amsterdam, The Netherlands, 7 February - Marh, (SPE paper 6775) Li Q, Peng Y C, Zhang S H, et al. Study on signal transmission tehniques in rotary steering drilling. Ata Petrolei Sinia. 7. 8(4): 8- (in Liu X S and Su Y N. Investigation on the transmission behavior of drilling fluid pulse signals. Oil Drilling & Prodution Tehnology.. (4): 8- (in Liu X S and Su Y N. Study on transmission veloity of mud pulse signals. Petroleum Drilling Tehniques.. 8(5): 4-6 (in Mar tin C A, Philo R M, Deker D P, et al. Innovative advanes in MWD. IADC/SPE Drilling Conferene held in Dallas, Texas, 5-8 February, 994 (SPE paper 756) Mon roe S P. Applying digital data-enoding tehniques to mud pulse telemetry. The 5th SPE Petroleum Computer Conferene held in Denier, Colorado, 5-8 June, 99 (SPE paper 36) Sh malhorst B, Brommundt E, Baumgart A, et al. Drilling dynamis in the presene of mud flow. IADC/SPE Drilling Conferene held in New Orleans, Louisiana, 3-5 February, (SPE paper 5936) Shi Z H and Liu X S. An analysis of drilling information transmission behavior in wellbores. Natural Gas Industry.. (5): 68-7 (in Was serman I, Hahn D, Hai Nguyen D, et al. Mud-pulse telemetry sees step-hange improvement with osillating shear valves. Oil & Gas Journal. 8. 6(4): Zha ng S H. New progress and development diretion of modern steering drilling tehniques. Ata Petrolei Sinia. 3. 4(3): 8-89 (in (Edited by Sun Yanhua)