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A time-driven transmission method for well logging networks

A time-driven transmission method for well logging networks consisting of multiple subnets. In this paper, we proposed a time-driven transmission method (TDTM) to improve the effi ciency and precision of logging networks. Using TDTM, we obtained well logging curves by fusing the depth acquired on the surface, and the data acquired in downhole instruments based on the synchronization timestamp. For the TDTM, the precision of time synchronization and the data fusion algorithm were two main factors infl uencing system errors. A piecewise fractal interpolation was proposed to fast fuse data in each interval of the logging curves. Intervals with similar characteristics in curves were extracted based on the change in the histogram of the interval. The TDTM is evaluated with a sonic curve, as an example. Experimental results showed that the fused data had little error, and the TDTM was effective and suitable for the logging networks. Data fusion, fractal interpolation, histogram, packet switch, timestamp Key words: speed, reduce time delay and optimize the router software 1 Introduction cannot improve the real-time performance effectively, and are Due to good performance in device interconnection, also very diffi cult to implement. transmission efficiency and universal application compared However, little research on this problem has been with those of other field buses, computer networks play published. In this paper, we presented a time-driven an increasingly important role in well logging systems, transmission method (TDTM) as an effective solution based and become one of the most important characteristics on accurate time synchronization and fast data fusion. During of the developing fifth generation network well logging data acquisition, the real-time transmission of parameter systems (Xiao et al, 2003; Tang, 2007; Wang et al, 2006). information from the surface equipment to downhole Although the switched Ethernet is a perfect solution for instruments was not required. The TDTM is used to reduce providing high throughput, short delay and low delay jitter network traffic and improve network efficiency for high to meet the demands of multi-measurement and control precision measurements. networks (Lian, 2001), the well logging network is a typical remote measurement and control network consisting of 2 Time-driven transmission model switched Ethernet and routers (Wu et al, 2005), due to strict environment limitations, such as wiring connection, 2.1 Data fl ow chart transmission distance, and device dimension. One simple Due to long delays and low transmission rates, the existing instance is that the surface equipment composes a control logging systems mainly work in a “request-reply” mode, subnet, the surface telemetry instruments (or surface gateway) as illustrated in Fig. 1(a) (Meng et al, 2003). The surface and the downhole wireline telemetry cartridge (or downhole equipment sends commands and the depth parameter as a gateway) compose the transmission subnet, and all the “request” to downhole instruments, and then the instruments downhole instruments compose an instrument subnet. We start to acquire data at the depth and transmit the data as a discovered that the logging network is a network focusing “reply” to the surface equipment after a delay. Finally, the on measurement, which needs to acquire accurate data and surface equipment obtains the logging curve, which describes record the corresponding measurement parameters, such as the change of measured data with depth. After transmitting time, depth, and length. The parameter data are transmitted commands to downhole instruments, the surface equipment is from the surface equipment to downhole instruments through inactive until receiving the acquired data or state information multi-hop networks. This process degrades the network from downhole instruments. With the increase of downhole utilization and increases delay, therefore it is impossible to sensors and parallel processing demand, the “request-reply” meet the real-time demands. Some methods to increase line mode becomes ineffi cient in logging applications. The well logging network using the TDTM consists of *Corresponding author. email: reeching@163.com the surface control center (SCC), the surface time-depth Received December 7, 2008 240 Pet.Sci.(2009)6:239-245 acquiring unit (TDAU), the surface time-depth-data fusion can obtain the fused depth-data sequence by the following unit (TDDFU), system time synchronization unit (STSU), equation: transmission network (TN), and downhole logging tools (DLT). The SCC forms the work command tables and sends df ()t them to downhole instruments by networks. The STSU Rg ()T accurately synchronizes each node’s clock of downhole (1) tT instruments and surface equipment. According to the predetermined depth interval, when hardware interrupts of rR sampling depth occur, the TDAU acquires the depth and -1 corresponding timestamp, and then obtains a time-depth The logging curve is r = g (f (d)) = h (d), but actually it is pair (t , d ). Many time-depth pairs compose the time-depth very difficult or impractical to obtain r = h (d). In order to i i sequence <t, d>. We assume that the time-depth sequence explain more clearly, we analyze the mapping relationship, <t, d> satisfies a function d = f (t). Generally, d = f (t) is assuming that the measured data r is one dimensional, as a piecewise linear function. Even if the intervals of depth shown in Fig. 2(a). interrupt are equal, when the speed of the logging cable In Fig. 2, (t , d ) and (t , d ) are from the time-depth i i j j changes, the intervals of timestamps are not always equal. sequence, (T , R ) and (T , R ) are from the time-data sequence, i i j j The downhole instruments record the measured data and (d , r ) and (d , r ) are to be obtained. Because the time- i i j j R corresponding to the time T and obtain the time- data sampling and the time-depth sampling are asynchronous, i i data pair (T , R ). Many time-data pairs compose a time- the sampling intervals of the two sequences are unequal. i i data sequence <T, R>. Then, the telemetry instruments Furthermore, the forms of g(T) and f(t) are unknown, so h(d) transmit the sequence <T, R> to the TDDFU. We assume has no explicit expression. Because T and t are different, i i that the time-data sequence <T, R> satisfies a function the goal of the depth-data fusion is to obtain the optimal R = g (T). Because of the difference in working mechanism (t, r) from (T, R) by an effective interpolation, as shown in of telemetry instruments, there are much data acquired at Fig. 2(b). unequal time intervals. The TDDFU fast fuses the <t, d> and <T, R> sequences, and finally obtains the depth-data sequence <d, r>, i.e., the logging curve. Fig. 1(b) shows the basic fl owchart of the TDTM. -1 r=g(f (d)) Depth panel Networks send data r=g(t) acquires depth to surface d d d i j Control center Networks send Network Tools acquire starts interactive commands to initialization i data operation downhole tools t (a) Basic fl owchart of the traditional model d=f(t) TDAU acquires STSU time-depth synchronizes time (a) Mapping of two sequences TDDFU fuses TN transmits DLT acquires time-depth-data time-data time-data Network SCC starts SCC generates TN transmits initialization interactive control command table command table (b) Basic fl owchart of the TDTM model r=g(t) Fig. 1 Well logging data fl owchart Compared with the “request-reply” mode, the TDTM uses the data fusion method based on the time synchronization unit i and data fusion unit. The TDDFU is an important module in R TDTM for fast and accurate data processing. In the following, we present a fast data fusion algorithm based on the analysis of the mapping model of time-depth-data. T t T t i i j j 2.2 Time-depth-data mapping (b) Time-data interpolation After the time is synchronized in the logging network, we Fig. 2 Time-depth-data mapping Pet.Sci.(2009)6:239-245 241 Usually, d = f (t) is piecewise linear, and r = h (d) and platform, the maximum Δt is equal to 10 ms, so the maximum r = g (t) have similar monotonicity, although they are in depth error achieves Δd=3.034mm, which is acceptable in different variable domains. This conclusion can be proven the logging system. Furthermore, the time delay in logging simply as follows: Because d = f (t) is piecewise linear, network is more than 100 ms, which results in a more serious we assume that it has the form d = f (t) = at+b in its linear depth error without the TDTM. interval, where a is a positive constant (if a is negative, 3.2 Infl uence of interpolation algorithm on error the conclusion will be the same), and b is an undetermined constant. Then, t=d/a−b/a and r=g(d/a−b/a)=h(d), so r = h (d) There are many interpolation algorithms providing and r = g (t) have a similar monotonicity. This conclusion is different complexities and levels of performance, such as very important to the selection of the interpolation algorithm bilinear, cubic spline, Lagrange, and Hermite interpolation. in the time domain to obtain (t , r ) from (T , R ). i i i i The optimum interpolation algorithm should retain the characteristics of the sequence to the greatest extent (T , R ) j j 3 TDTM error analysis (Burnside and Parks, 1990). The data acquired by telemetric instruments, such as sonic waves, gamma rays, and natural We focus on the main factors infl uencing the performance electric potentials, refl ect the attributes of geological objects. of the TDTM. In fact, the data processing shows that t and The existing literature and the actual analysis results show T are not always equal, and do not satisfy Eq. (1). We can that different logging curves have different characteristics, describe their relation by the following equation: and most logging curves have obvious fractal characteristics in the entire depth domain (Li and Xiao, 2002; Li, 2005; Lu (2) tT ' ˇ t' s and Li, 1996), so fractal interpolation can be used to improve the resolution. where Δt is the error resulting from synchronization, and Δs is Usually, fractal dimension is a measure to determine the error from the asynchronous data acquisition of the surface whether the logging curve has fractal characteristics. equipment and downhole instruments. Thereby, there are two Moreover, the fractal characteristics of logging curves change factors infl uencing the performance of the TDTM. One factor with geological structure. Well logging curves have different is the precision of the network time synchronization, and the fractal characteristics in different depth intervals, even in the other is the data fusion algorithm. Much work has been done same well (Hewett, 1986; Liu et al, 2004). Table 1 gives the on the methods to highly synchronize the network time. In statistics of fractal dimensions of different interval lengths this paper, an effi cient interpolation algorithm was proposed from a sonic sequence as shown in Fig. 4(a). This sonic to minimize the error from asynchronous acquisition. The sequence is recorded from the depth 2079 m to 2487 m, discussion in the following section will focus on the infl uence including 2675 points. The fractal dimensions are calculated of Δt and Δs. by a box dimension algorithm. 3.1 Time synchronization error We suppose that there is an absolute accurate time t, and Fractal dimensions of different interval lengths Table 1 the time synchronization error between surface equipment and downhole instruments is Δt. When (t , d ) is acquired on i i Interval length Max. Min. Average the surface at t , but (t +Δt, r ) is recorded in the downhole, i i i so they will be mistaken as the measurement data at 50 1.1551 1.0577 1.1192 different depth. If Δt increases, it will result in an increase of depth error. In the TDTM, t is stored in a timestamp 100 1.2042 1.1373 1.1694 field of the packet. There are two basic attributes related to the timestamp. One is time granularity, which indicates 150 1.2357 1.1743 1.2055 the resolution of the system timer. In our experiment, the 200 1.2557 1.1977 1.2309 granularity of the platform named ELIS-800 is 1.6 μs, which means that the time counter increases by one per 1.6 μs. The 2675 1.52 1.52 1.52 other attribute is the bit number allocated for storage, and the bit number of ELIS-800 is set to 32 bit. Generally, the cable speed, defined by v, is a piecewise From Table 1, we can see that the fractal dimension is not constant less than 30 m/min. The depth d and time t satisfy a constant and shows the different fractal features in different the following equation: intervals. Therefore, piecewise fractal interpolation should be used to retain local characteristics and improve accuracy of dt ()  vdt d (3) data fusion. Therefore, the depth error is Δd = vΔt. When the time 4 Fast data fusion error Δt maintains a specific value, if v increases, Δd will become greater. For example, in PEXWL (Platform Express Existing literature has focused on calculating the fractal Integrated Wireline Logging), the cable travels at a speed of dimension, discussing the performance of interpolation v =3600 ft/hr = 0.3048 mm/ms. In the ELIS-800 experimental function, and deriving the error of fractal interpolation 242 Pet.Sci.(2009)6:239-245 accumulative drift from interval φ to φ is defined by l n function (Li and Xiao, 2002; Li, 2005; Sha and Liu, 2004). Directly calculating the fractal dimension in real-time analysis Fl (,n) VV , where n > l. If any one condition in the ¦ ii 1 of the logging curves has some disadvantages, such as large il iterations, poor real-time performance and high computation following equations is satisfi ed: load in the interpolation interval. We present a fast data fusion algorithm based on the change in the histogram of time- ­ Pl ( ,n) (P P )/! 2˜ D  (P P )/ 2 max min max min data. This algorithm has more advantages, such as retaining Pl ( ,n) (P P )/ 2 (P P )/ (2D ) local characteristics, reducing the usage of resources, and ° max min max min (5) improving computation speed. Fl (,n) (F F ) /! 2˜ E (F F ) / 2 ° maxmin maxmin The histogram of data with the same fractal characteristics Fl ( ,n) (F F )/ 2 (F F )/ (2E ) max min max min usually has a dense, symmetrical or quasi-symmetrical ¯ distribution, such as normal distribution or box-type (Li and Xiao, 2002). Therefore, we propose a method to extract the where, PP  min (l,l 1)," ,P(l,n 1) , min intervals for piecewise interpolation based on the change PP  max (l,l 1)," ,P(l,n 1) , max of histogram in the distribution features. In each extracted FF  min (l,l 1)," ,F (l,n 1) , interval, the self-affi ne fractal interpolation method is used to min obtain a high-resolution curve. FF  max (,ll 1)," ,F(,ln 1) , then φ has a different max distribution characteristic from φ , ..., φ , and a new l n-1 4.1 Logging curve piecewise extraction piecewise fractal interpolation starts in φ . Peak and variance 4.1.1 Extract statistical parameter accumulative drift are used to detect whether current Firstly, we obtained the histogram of M logging data intervals have similar characteristics or have gradual changes R in the interval φ , and then calculated the mean μ and i n n compared with the previous interval. variance σ of R . Then, we extracted the highest peak P in n i m 4.2 Piecewise fractal interpolation and fusion the histogram and its corresponding measurement value y . Supposing that there are M points in the interpolation Finally, we calculated the peak drift y −y compared with m m-1 interval φ and N data points in the mapping interval, the the previous interpolation interval φ . n-1 general form of the one-dimensional self-affi ne interpolation 4.1.2 Determination of PP-skewness and kurtosis function is as follows: The PP-skewness and kurtosis are two properties of the stochastic variable distribution. The PP-skewness defi ned by k is a measure of symmetry distribution (Chen and Cui, 2004). ª xº ª a 0º ª xº ª e º i i , where d  1 The PP-kurtosis defi ned by g is a measure of the density of « » « » « » « » y c d y f ¬ ¼ ¬ i i¼ ¬ ¼ ¬ i¼ the probability distribution. The k of normal distribution is usually 0, and g is 3. If k is far away from 0 or g far away The detailed procedure of iterative interpolation can refer from 3, we can conclude that it may be much different from to two papers (Manousopoulos et al, 2008; Mazel and Hayes, the normal distribution. The PP-skewness and kurtosis of 1992). The piecewise fractal interpolation interval φ slides ... stochastic logging data R , R , , R in φ are calculated 1 2 m n continuously with receiving the real-time data. It is therefore according to the following equation: the so-called sliding window piecewise fractal interpolation. A higher-resolution time-data curve <T ', R'> is obtained by mm piecewise fractal interpolation. However, the expected t in 32 2 §· kR R R R ni¦¦¨¸i Fig. 2 may not be at T in the <T ', R'>. To solve this problem, ii 11©¹ the neighboring linear interpolation is taken to obtain (t , r ) i i (4) mm ° 42 §· from the two nearest values, i.e., the previous (T ' , R' ) and m m gR R R R ° ¦¦ ni ¨¸i the next (T ' , R' ). Therefore, the fusion curve  is ! dr , n n ¯ ii 11©¹ obtained from <t, d> and <t, r>. 5 Simulation and results where RR . If a large change exists from k <0 to ¦ n-1 In order to evaluate the time-depth-data fusion algorithm, i 1 k >0, or from k >0 to k <0, which is a jump round the zero n n-1 n a sonic curve acquired in the depth of 2079-2487 m is given point, a new fractal interpolation should start in the interval as a reference sequence <d, r>, whose depth sampling interval φ . n is 0.1524 m. The simulation of depth-data fusion adopts the model shown in Fig. 3. After obtaining the time-depth 4.1.3 Determination of peak and variance accumulative sequence <t, d> and time-data sequence <T, R>, the ! dr , drift sequence is gained by piecewise fractal interpolation and The peak accumulative drift from interval φ to φ is l n fusion, where the threshold parameters in Eq. (5) are set to α = 1.25, β = 2. Finally, the error curve 'dr ,!  between the defined by Pl (,n)  y y , where n > l, and variance ¦ ii 1 <d, r> and  sequences is calculated. ! dr , il Pet.Sci.(2009)6:239-245 243 Time-depth sequence Depth interrupt Time-depth x 10 trigger sequence Reference Depth-record Depth-record Clock curve fusing sequence Time driven Time-record recorder sequence Subtracter Error curve Fig. 3 Flowchart of time-depth-data simulation model 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 Depth, m In order to compare the performance of piecewise fractal interpolation, we only use a linear interpolation method to (b) Time-depth sequence obtain (t , r ) from the two nearest values, i.e., the previous i i (T , R ) and the next (T , R ) shown in Fig. 2, and then obtain i i j j the other fused curve ! dr , and corresponding error curve Time-data sequence 'dr ,! . The experimental results are illustrated from Fig. 4(b) to Fig. 4(i). From the results shown in Fig. 4, the reference sonic curve shown in Fig. 4(a) has a large and continuous amplitude change at the depth of approximately 2200 m. When the time- depth sequence is linear, the time-data curve has a similar monotonic property to the reference sequence as shown in -200 Fig. 4(b) and Fig. 4(c). The variance and peak accumulative drift have a large jump at the depth of approximately 2200 m, -400 which indicates an evident change in distribution shown in Fig. 4(d) and Fig. 4(e). The PP-skewness and PP-kurtosis (both -600 in a small amplitude) curves shown in Fig. 4(f) accord with the characteristics of dense distribution. After the piecewise -800 fractal interpolation and fusion, the error between the fused -1000 curve shown in Fig. 4(g) and the reference curve is smaller 0 2468 10 12 14 16 18 as a whole, compared with simple linear interpolation, as 4 x 10 Time, ms illustrated in Fig. 4(h) and Fig. 4(i). (c) Time-data sequence Reference curve -100 -200 -200 -400 -300 -600 -400 -800 -500 -1000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 Depth, m Depth, m (d) Peak accumulative drift (a) Reference sonic curve Data, mv Peak position accumulative drift Data, mv Time, ms 244 Pet.Sci.(2009)6:239-245 x 10 3 1 -1 -2 -3 -4 -1 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 Depth, m Depth, m (h) Error curve'dr ,! (e) Variance accumulative drift 0.2 0.1 -0.1 -0.2 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 -10 Depth, m -20 0.12 0.1 -30 0.08 0.06 -40 0.04 -50 0.02 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 Depth, m 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 Depth, m 'dr ,! (i) Error curve (f) PP-skewness and PP-kurtosis curve Fig. 4 Time-depth-data fusion results If the fractal interpolation is not used in each interval, but Depth-data fused sequence in the whole depth domain of the acquired data, there will be a long delay. For example, the delay for the sonic curve shown in Fig. 4(a) includes two parts: 1) The first part T is the time waiting for acquiring all the data of 2675 depth points. If the speed of the cable is 30 m/min, T is (2487- 2079)/30×60=816 seconds. 2) The second part is the time of -200 interpolation for all sampling points T . On our simulation platform, T is 240 seconds. However, the time delay of -400 the piecewise fractal interpolation proposed in this paper is approximately 15 seconds on the same platform. Therefore, -600 the piecewise fractal interpolation can improve the real-time processing for the TDTM and logging networks. -800 6 Conclusions -1000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 The time-driven transmission method does not need a Depth, m high-level real-time network. However, the well logging (g) Fused depth-data sequence network should keep an accurate synchronization time to Data, mv Kurtosis Skewness Variance accumulative drift Error, mv Error, mv Pet.Sci.(2009)6:239-245 245 Control Systems Magazine. 2001. 21(1): 66-83 reduce depth error, which can be achieved with the existing Li C F. Some remarks on application of fractal analyses in well logging time synchronization solutions. Time synchronization data. Well Logging Technology. 2005. 29(1): 15-20 (in Chinese) is a main factor for the TDTM to decrease errors. The Liu H Q, Peng S M, Zhou Y Y, et al. Discrimination of natural fractures method to extract fractal intervals based on the change of using well logging curve unit. Journal of China University of histogram characteristics is very effective. The piecewise Geosciences. 2004. 15(4): 372-378 fractal interpolation can obtain high-resolution sequences Li Y S and Xiao X C. A study on the fractal characterization of sonic for data fusion, which meets the demand of high- logging signal. Signal Processing. 2002. 18(2): 186-188 (in Chinese) precision transmission and accurate logging interpretation. Lu J A and Li Z B. The self-similarity study of well logging curves. Well Experimental results show that the fused data have less errors Logging Technology. 1996. 6(20): 422-427 (in Chinese) and the time-driven transmission method is effective and Man ousopoulos P, Drakopoulos V and Theoharis T. Curve fitting suitable for the logging networks. by fractal interpolation. Lecture Notes in Computer Science, Transactions on Computational Science I. Berlin: Springer. 2008. 4750: 85-103 Acknowledgements Maz el D S and Hayes M H. Using iterated function systems to model This work was supported by the China National Offshore discrete sequences. IEEE Transactions on Signal Processing. 1992. Oil Corporation under the High Speed Logging Transmission 40(7): 1724-1734 Network based on OFDM and Ethernet Program, and Men g G S, Zhang L, Zhang C, et al. The principle of the WTS surface communication unit in ECLIPS-5700 logging system. Tuha Oil & also supported by the UESTC-COSL Joint Laboratory of Gas. 2003. 8(4): 354-357 (in Chinese) Electrical Logging. The authors would like to thank Dr. Meng Sha Z and Liu Y L. The error of FIF. Applied Mathematics: A Journal of and Mr. Jin for providing the logging data. Chinese Universities (Ser. A). 2004. 19(2): 193-202 (in Chinese) Tang T Z. Technical present and future developing consideration on References EILog logging system. Well Logging Technology. 2007. 31(2): 99- Burn side D and Parks T W. Amplitude bound interpolation of sonic well- 102 (in Chinese) log data. Acoustics, Speech and Signal Processing. 1990. 4: 1933- Wan g R, Liu Z Y and Zhang Y G. Design and implementation of an oil- 1936 (ICASSP-90) well-logging data transport system. Computer Engineering. 2006. Che n G L and Cui H J. The testing for normality based on PP-skewness 32(4): 236-240 (in Chinese) and PP-kurtosis in EV model. Mathematica Applicata. 2004. 17(1): Wu W B, Yao J H and Shen J W. Real-time long range transmission of 16-21 (in Chinese) log data through GPRS. Petroleum Instruments. 2005. 19(4): 72-73 Hew ett T A. Fractal distributions of reservoir heterogeneity and their (in Chinese) infl uence on fl uid transport. Society of Petroleum Engineers Annual Xia o L Z, Xie R H, Chai X Y, et al. Well logging technology for the Technical Conference and Exhibition. New Orleans, USA. 1986 new century: network-based logging technology. Well Logging Lia n F L, Moyne J R and Tilbury D M. Performance evaluation of Technology. 2003. 27(1): 6-10 (in Chinese) control networks: Ethernet, ControlNet, and DeviceNet. IEEE (Edited by Hao Jie) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Petroleum Science Springer Journals

A time-driven transmission method for well logging networks

Wu, Ruiqing; Chen, Wei; Chen, Tianqi; Li, Qun
Petroleum Science , Volume 6 (3) – Jul 23, 2009
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Springer Journals
Copyright
Copyright © 2009 by China University of Petroleum (Beijing) and Springer-Verlag GmbH
Subject
Earth Sciences; Mineral Resources; Industrial Chemistry/Chemical Engineering; Industrial and Production Engineering; Energy Economics
ISSN
1672-5107
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1995-8226
DOI
10.1007/s12182-009-0038-4
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Abstract

consisting of multiple subnets. In this paper, we proposed a time-driven transmission method (TDTM) to improve the effi ciency and precision of logging networks. Using TDTM, we obtained well logging curves by fusing the depth acquired on the surface, and the data acquired in downhole instruments based on the synchronization timestamp. For the TDTM, the precision of time synchronization and the data fusion algorithm were two main factors infl uencing system errors. A piecewise fractal interpolation was proposed to fast fuse data in each interval of the logging curves. Intervals with similar characteristics in curves were extracted based on the change in the histogram of the interval. The TDTM is evaluated with a sonic curve, as an example. Experimental results showed that the fused data had little error, and the TDTM was effective and suitable for the logging networks. Data fusion, fractal interpolation, histogram, packet switch, timestamp Key words: speed, reduce time delay and optimize the router software 1 Introduction cannot improve the real-time performance effectively, and are Due to good performance in device interconnection, also very diffi cult to implement. transmission efficiency and universal application compared However, little research on this problem has been with those of other field buses, computer networks play published. In this paper, we presented a time-driven an increasingly important role in well logging systems, transmission method (TDTM) as an effective solution based and become one of the most important characteristics on accurate time synchronization and fast data fusion. During of the developing fifth generation network well logging data acquisition, the real-time transmission of parameter systems (Xiao et al, 2003; Tang, 2007; Wang et al, 2006). information from the surface equipment to downhole Although the switched Ethernet is a perfect solution for instruments was not required. The TDTM is used to reduce providing high throughput, short delay and low delay jitter network traffic and improve network efficiency for high to meet the demands of multi-measurement and control precision measurements. networks (Lian, 2001), the well logging network is a typical remote measurement and control network consisting of 2 Time-driven transmission model switched Ethernet and routers (Wu et al, 2005), due to strict environment limitations, such as wiring connection, 2.1 Data fl ow chart transmission distance, and device dimension. One simple Due to long delays and low transmission rates, the existing instance is that the surface equipment composes a control logging systems mainly work in a “request-reply” mode, subnet, the surface telemetry instruments (or surface gateway) as illustrated in Fig. 1(a) (Meng et al, 2003). The surface and the downhole wireline telemetry cartridge (or downhole equipment sends commands and the depth parameter as a gateway) compose the transmission subnet, and all the “request” to downhole instruments, and then the instruments downhole instruments compose an instrument subnet. We start to acquire data at the depth and transmit the data as a discovered that the logging network is a network focusing “reply” to the surface equipment after a delay. Finally, the on measurement, which needs to acquire accurate data and surface equipment obtains the logging curve, which describes record the corresponding measurement parameters, such as the change of measured data with depth. After transmitting time, depth, and length. The parameter data are transmitted commands to downhole instruments, the surface equipment is from the surface equipment to downhole instruments through inactive until receiving the acquired data or state information multi-hop networks. This process degrades the network from downhole instruments. With the increase of downhole utilization and increases delay, therefore it is impossible to sensors and parallel processing demand, the “request-reply” meet the real-time demands. Some methods to increase line mode becomes ineffi cient in logging applications. The well logging network using the TDTM consists of *Corresponding author. email: reeching@163.com the surface control center (SCC), the surface time-depth Received December 7, 2008 240 Pet.Sci.(2009)6:239-245 acquiring unit (TDAU), the surface time-depth-data fusion can obtain the fused depth-data sequence by the following unit (TDDFU), system time synchronization unit (STSU), equation: transmission network (TN), and downhole logging tools (DLT). The SCC forms the work command tables and sends df ()t them to downhole instruments by networks. The STSU Rg ()T accurately synchronizes each node’s clock of downhole (1) tT instruments and surface equipment. According to the predetermined depth interval, when hardware interrupts of rR sampling depth occur, the TDAU acquires the depth and -1 corresponding timestamp, and then obtains a time-depth The logging curve is r = g (f (d)) = h (d), but actually it is pair (t , d ). Many time-depth pairs compose the time-depth very difficult or impractical to obtain r = h (d). In order to i i sequence <t, d>. We assume that the time-depth sequence explain more clearly, we analyze the mapping relationship, <t, d> satisfies a function d = f (t). Generally, d = f (t) is assuming that the measured data r is one dimensional, as a piecewise linear function. Even if the intervals of depth shown in Fig. 2(a). interrupt are equal, when the speed of the logging cable In Fig. 2, (t , d ) and (t , d ) are from the time-depth i i j j changes, the intervals of timestamps are not always equal. sequence, (T , R ) and (T , R ) are from the time-data sequence, i i j j The downhole instruments record the measured data and (d , r ) and (d , r ) are to be obtained. Because the time- i i j j R corresponding to the time T and obtain the time- data sampling and the time-depth sampling are asynchronous, i i data pair (T , R ). Many time-data pairs compose a time- the sampling intervals of the two sequences are unequal. i i data sequence <T, R>. Then, the telemetry instruments Furthermore, the forms of g(T) and f(t) are unknown, so h(d) transmit the sequence <T, R> to the TDDFU. We assume has no explicit expression. Because T and t are different, i i that the time-data sequence <T, R> satisfies a function the goal of the depth-data fusion is to obtain the optimal R = g (T). Because of the difference in working mechanism (t, r) from (T, R) by an effective interpolation, as shown in of telemetry instruments, there are much data acquired at Fig. 2(b). unequal time intervals. The TDDFU fast fuses the <t, d> and <T, R> sequences, and finally obtains the depth-data sequence <d, r>, i.e., the logging curve. Fig. 1(b) shows the basic fl owchart of the TDTM. -1 r=g(f (d)) Depth panel Networks send data r=g(t) acquires depth to surface d d d i j Control center Networks send Network Tools acquire starts interactive commands to initialization i data operation downhole tools t (a) Basic fl owchart of the traditional model d=f(t) TDAU acquires STSU time-depth synchronizes time (a) Mapping of two sequences TDDFU fuses TN transmits DLT acquires time-depth-data time-data time-data Network SCC starts SCC generates TN transmits initialization interactive control command table command table (b) Basic fl owchart of the TDTM model r=g(t) Fig. 1 Well logging data fl owchart Compared with the “request-reply” mode, the TDTM uses the data fusion method based on the time synchronization unit i and data fusion unit. The TDDFU is an important module in R TDTM for fast and accurate data processing. In the following, we present a fast data fusion algorithm based on the analysis of the mapping model of time-depth-data. T t T t i i j j 2.2 Time-depth-data mapping (b) Time-data interpolation After the time is synchronized in the logging network, we Fig. 2 Time-depth-data mapping Pet.Sci.(2009)6:239-245 241 Usually, d = f (t) is piecewise linear, and r = h (d) and platform, the maximum Δt is equal to 10 ms, so the maximum r = g (t) have similar monotonicity, although they are in depth error achieves Δd=3.034mm, which is acceptable in different variable domains. This conclusion can be proven the logging system. Furthermore, the time delay in logging simply as follows: Because d = f (t) is piecewise linear, network is more than 100 ms, which results in a more serious we assume that it has the form d = f (t) = at+b in its linear depth error without the TDTM. interval, where a is a positive constant (if a is negative, 3.2 Infl uence of interpolation algorithm on error the conclusion will be the same), and b is an undetermined constant. Then, t=d/a−b/a and r=g(d/a−b/a)=h(d), so r = h (d) There are many interpolation algorithms providing and r = g (t) have a similar monotonicity. This conclusion is different complexities and levels of performance, such as very important to the selection of the interpolation algorithm bilinear, cubic spline, Lagrange, and Hermite interpolation. in the time domain to obtain (t , r ) from (T , R ). i i i i The optimum interpolation algorithm should retain the characteristics of the sequence to the greatest extent (T , R ) j j 3 TDTM error analysis (Burnside and Parks, 1990). The data acquired by telemetric instruments, such as sonic waves, gamma rays, and natural We focus on the main factors infl uencing the performance electric potentials, refl ect the attributes of geological objects. of the TDTM. In fact, the data processing shows that t and The existing literature and the actual analysis results show T are not always equal, and do not satisfy Eq. (1). We can that different logging curves have different characteristics, describe their relation by the following equation: and most logging curves have obvious fractal characteristics in the entire depth domain (Li and Xiao, 2002; Li, 2005; Lu (2) tT ' ˇ t' s and Li, 1996), so fractal interpolation can be used to improve the resolution. where Δt is the error resulting from synchronization, and Δs is Usually, fractal dimension is a measure to determine the error from the asynchronous data acquisition of the surface whether the logging curve has fractal characteristics. equipment and downhole instruments. Thereby, there are two Moreover, the fractal characteristics of logging curves change factors infl uencing the performance of the TDTM. One factor with geological structure. Well logging curves have different is the precision of the network time synchronization, and the fractal characteristics in different depth intervals, even in the other is the data fusion algorithm. Much work has been done same well (Hewett, 1986; Liu et al, 2004). Table 1 gives the on the methods to highly synchronize the network time. In statistics of fractal dimensions of different interval lengths this paper, an effi cient interpolation algorithm was proposed from a sonic sequence as shown in Fig. 4(a). This sonic to minimize the error from asynchronous acquisition. The sequence is recorded from the depth 2079 m to 2487 m, discussion in the following section will focus on the infl uence including 2675 points. The fractal dimensions are calculated of Δt and Δs. by a box dimension algorithm. 3.1 Time synchronization error We suppose that there is an absolute accurate time t, and Fractal dimensions of different interval lengths Table 1 the time synchronization error between surface equipment and downhole instruments is Δt. When (t , d ) is acquired on i i Interval length Max. Min. Average the surface at t , but (t +Δt, r ) is recorded in the downhole, i i i so they will be mistaken as the measurement data at 50 1.1551 1.0577 1.1192 different depth. If Δt increases, it will result in an increase of depth error. In the TDTM, t is stored in a timestamp 100 1.2042 1.1373 1.1694 field of the packet. There are two basic attributes related to the timestamp. One is time granularity, which indicates 150 1.2357 1.1743 1.2055 the resolution of the system timer. In our experiment, the 200 1.2557 1.1977 1.2309 granularity of the platform named ELIS-800 is 1.6 μs, which means that the time counter increases by one per 1.6 μs. The 2675 1.52 1.52 1.52 other attribute is the bit number allocated for storage, and the bit number of ELIS-800 is set to 32 bit. Generally, the cable speed, defined by v, is a piecewise From Table 1, we can see that the fractal dimension is not constant less than 30 m/min. The depth d and time t satisfy a constant and shows the different fractal features in different the following equation: intervals. Therefore, piecewise fractal interpolation should be used to retain local characteristics and improve accuracy of dt ()  vdt d (3) data fusion. Therefore, the depth error is Δd = vΔt. When the time 4 Fast data fusion error Δt maintains a specific value, if v increases, Δd will become greater. For example, in PEXWL (Platform Express Existing literature has focused on calculating the fractal Integrated Wireline Logging), the cable travels at a speed of dimension, discussing the performance of interpolation v =3600 ft/hr = 0.3048 mm/ms. In the ELIS-800 experimental function, and deriving the error of fractal interpolation 242 Pet.Sci.(2009)6:239-245 accumulative drift from interval φ to φ is defined by l n function (Li and Xiao, 2002; Li, 2005; Sha and Liu, 2004). Directly calculating the fractal dimension in real-time analysis Fl (,n) VV , where n > l. If any one condition in the ¦ ii 1 of the logging curves has some disadvantages, such as large il iterations, poor real-time performance and high computation following equations is satisfi ed: load in the interpolation interval. We present a fast data fusion algorithm based on the change in the histogram of time- ­ Pl ( ,n) (P P )/! 2˜ D  (P P )/ 2 max min max min data. This algorithm has more advantages, such as retaining Pl ( ,n) (P P )/ 2 (P P )/ (2D ) local characteristics, reducing the usage of resources, and ° max min max min (5) improving computation speed. Fl (,n) (F F ) /! 2˜ E (F F ) / 2 ° maxmin maxmin The histogram of data with the same fractal characteristics Fl ( ,n) (F F )/ 2 (F F )/ (2E ) max min max min usually has a dense, symmetrical or quasi-symmetrical ¯ distribution, such as normal distribution or box-type (Li and Xiao, 2002). Therefore, we propose a method to extract the where, PP  min (l,l 1)," ,P(l,n 1) , min intervals for piecewise interpolation based on the change PP  max (l,l 1)," ,P(l,n 1) , max of histogram in the distribution features. In each extracted FF  min (l,l 1)," ,F (l,n 1) , interval, the self-affi ne fractal interpolation method is used to min obtain a high-resolution curve. FF  max (,ll 1)," ,F(,ln 1) , then φ has a different max distribution characteristic from φ , ..., φ , and a new l n-1 4.1 Logging curve piecewise extraction piecewise fractal interpolation starts in φ . Peak and variance 4.1.1 Extract statistical parameter accumulative drift are used to detect whether current Firstly, we obtained the histogram of M logging data intervals have similar characteristics or have gradual changes R in the interval φ , and then calculated the mean μ and i n n compared with the previous interval. variance σ of R . Then, we extracted the highest peak P in n i m 4.2 Piecewise fractal interpolation and fusion the histogram and its corresponding measurement value y . Supposing that there are M points in the interpolation Finally, we calculated the peak drift y −y compared with m m-1 interval φ and N data points in the mapping interval, the the previous interpolation interval φ . n-1 general form of the one-dimensional self-affi ne interpolation 4.1.2 Determination of PP-skewness and kurtosis function is as follows: The PP-skewness and kurtosis are two properties of the stochastic variable distribution. The PP-skewness defi ned by k is a measure of symmetry distribution (Chen and Cui, 2004). ª xº ª a 0º ª xº ª e º i i , where d  1 The PP-kurtosis defi ned by g is a measure of the density of « » « » « » « » y c d y f ¬ ¼ ¬ i i¼ ¬ ¼ ¬ i¼ the probability distribution. The k of normal distribution is usually 0, and g is 3. If k is far away from 0 or g far away The detailed procedure of iterative interpolation can refer from 3, we can conclude that it may be much different from to two papers (Manousopoulos et al, 2008; Mazel and Hayes, the normal distribution. The PP-skewness and kurtosis of 1992). The piecewise fractal interpolation interval φ slides ... stochastic logging data R , R , , R in φ are calculated 1 2 m n continuously with receiving the real-time data. It is therefore according to the following equation: the so-called sliding window piecewise fractal interpolation. A higher-resolution time-data curve <T ', R'> is obtained by mm piecewise fractal interpolation. However, the expected t in 32 2 §· kR R R R ni¦¦¨¸i Fig. 2 may not be at T in the <T ', R'>. To solve this problem, ii 11©¹ the neighboring linear interpolation is taken to obtain (t , r ) i i (4) mm ° 42 §· from the two nearest values, i.e., the previous (T ' , R' ) and m m gR R R R ° ¦¦ ni ¨¸i the next (T ' , R' ). Therefore, the fusion curve  is ! dr , n n ¯ ii 11©¹ obtained from <t, d> and <t, r>. 5 Simulation and results where RR . If a large change exists from k <0 to ¦ n-1 In order to evaluate the time-depth-data fusion algorithm, i 1 k >0, or from k >0 to k <0, which is a jump round the zero n n-1 n a sonic curve acquired in the depth of 2079-2487 m is given point, a new fractal interpolation should start in the interval as a reference sequence <d, r>, whose depth sampling interval φ . n is 0.1524 m. The simulation of depth-data fusion adopts the model shown in Fig. 3. After obtaining the time-depth 4.1.3 Determination of peak and variance accumulative sequence <t, d> and time-data sequence <T, R>, the ! dr , drift sequence is gained by piecewise fractal interpolation and The peak accumulative drift from interval φ to φ is l n fusion, where the threshold parameters in Eq. (5) are set to α = 1.25, β = 2. Finally, the error curve 'dr ,!  between the defined by Pl (,n)  y y , where n > l, and variance ¦ ii 1 <d, r> and  sequences is calculated. ! dr , il Pet.Sci.(2009)6:239-245 243 Time-depth sequence Depth interrupt Time-depth x 10 trigger sequence Reference Depth-record Depth-record Clock curve fusing sequence Time driven Time-record recorder sequence Subtracter Error curve Fig. 3 Flowchart of time-depth-data simulation model 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 Depth, m In order to compare the performance of piecewise fractal interpolation, we only use a linear interpolation method to (b) Time-depth sequence obtain (t , r ) from the two nearest values, i.e., the previous i i (T , R ) and the next (T , R ) shown in Fig. 2, and then obtain i i j j the other fused curve ! dr , and corresponding error curve Time-data sequence 'dr ,! . The experimental results are illustrated from Fig. 4(b) to Fig. 4(i). From the results shown in Fig. 4, the reference sonic curve shown in Fig. 4(a) has a large and continuous amplitude change at the depth of approximately 2200 m. When the time- depth sequence is linear, the time-data curve has a similar monotonic property to the reference sequence as shown in -200 Fig. 4(b) and Fig. 4(c). The variance and peak accumulative drift have a large jump at the depth of approximately 2200 m, -400 which indicates an evident change in distribution shown in Fig. 4(d) and Fig. 4(e). The PP-skewness and PP-kurtosis (both -600 in a small amplitude) curves shown in Fig. 4(f) accord with the characteristics of dense distribution. After the piecewise -800 fractal interpolation and fusion, the error between the fused -1000 curve shown in Fig. 4(g) and the reference curve is smaller 0 2468 10 12 14 16 18 as a whole, compared with simple linear interpolation, as 4 x 10 Time, ms illustrated in Fig. 4(h) and Fig. 4(i). (c) Time-data sequence Reference curve -100 -200 -200 -400 -300 -600 -400 -800 -500 -1000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 Depth, m Depth, m (d) Peak accumulative drift (a) Reference sonic curve Data, mv Peak position accumulative drift Data, mv Time, ms 244 Pet.Sci.(2009)6:239-245 x 10 3 1 -1 -2 -3 -4 -1 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 Depth, m Depth, m (h) Error curve'dr ,! (e) Variance accumulative drift 0.2 0.1 -0.1 -0.2 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 -10 Depth, m -20 0.12 0.1 -30 0.08 0.06 -40 0.04 -50 0.02 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 Depth, m 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 Depth, m 'dr ,! (i) Error curve (f) PP-skewness and PP-kurtosis curve Fig. 4 Time-depth-data fusion results If the fractal interpolation is not used in each interval, but Depth-data fused sequence in the whole depth domain of the acquired data, there will be a long delay. For example, the delay for the sonic curve shown in Fig. 4(a) includes two parts: 1) The first part T is the time waiting for acquiring all the data of 2675 depth points. If the speed of the cable is 30 m/min, T is (2487- 2079)/30×60=816 seconds. 2) The second part is the time of -200 interpolation for all sampling points T . On our simulation platform, T is 240 seconds. However, the time delay of -400 the piecewise fractal interpolation proposed in this paper is approximately 15 seconds on the same platform. Therefore, -600 the piecewise fractal interpolation can improve the real-time processing for the TDTM and logging networks. -800 6 Conclusions -1000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 The time-driven transmission method does not need a Depth, m high-level real-time network. However, the well logging (g) Fused depth-data sequence network should keep an accurate synchronization time to Data, mv Kurtosis Skewness Variance accumulative drift Error, mv Error, mv Pet.Sci.(2009)6:239-245 245 Control Systems Magazine. 2001. 21(1): 66-83 reduce depth error, which can be achieved with the existing Li C F. Some remarks on application of fractal analyses in well logging time synchronization solutions. Time synchronization data. Well Logging Technology. 2005. 29(1): 15-20 (in Chinese) is a main factor for the TDTM to decrease errors. The Liu H Q, Peng S M, Zhou Y Y, et al. Discrimination of natural fractures method to extract fractal intervals based on the change of using well logging curve unit. Journal of China University of histogram characteristics is very effective. The piecewise Geosciences. 2004. 15(4): 372-378 fractal interpolation can obtain high-resolution sequences Li Y S and Xiao X C. A study on the fractal characterization of sonic for data fusion, which meets the demand of high- logging signal. Signal Processing. 2002. 18(2): 186-188 (in Chinese) precision transmission and accurate logging interpretation. Lu J A and Li Z B. The self-similarity study of well logging curves. Well Experimental results show that the fused data have less errors Logging Technology. 1996. 6(20): 422-427 (in Chinese) and the time-driven transmission method is effective and Man ousopoulos P, Drakopoulos V and Theoharis T. Curve fitting suitable for the logging networks. by fractal interpolation. Lecture Notes in Computer Science, Transactions on Computational Science I. Berlin: Springer. 2008. 4750: 85-103 Acknowledgements Maz el D S and Hayes M H. Using iterated function systems to model This work was supported by the China National Offshore discrete sequences. IEEE Transactions on Signal Processing. 1992. Oil Corporation under the High Speed Logging Transmission 40(7): 1724-1734 Network based on OFDM and Ethernet Program, and Men g G S, Zhang L, Zhang C, et al. The principle of the WTS surface communication unit in ECLIPS-5700 logging system. Tuha Oil & also supported by the UESTC-COSL Joint Laboratory of Gas. 2003. 8(4): 354-357 (in Chinese) Electrical Logging. The authors would like to thank Dr. Meng Sha Z and Liu Y L. The error of FIF. Applied Mathematics: A Journal of and Mr. Jin for providing the logging data. Chinese Universities (Ser. A). 2004. 19(2): 193-202 (in Chinese) Tang T Z. Technical present and future developing consideration on References EILog logging system. Well Logging Technology. 2007. 31(2): 99- Burn side D and Parks T W. Amplitude bound interpolation of sonic well- 102 (in Chinese) log data. Acoustics, Speech and Signal Processing. 1990. 4: 1933- Wan g R, Liu Z Y and Zhang Y G. Design and implementation of an oil- 1936 (ICASSP-90) well-logging data transport system. Computer Engineering. 2006. Che n G L and Cui H J. The testing for normality based on PP-skewness 32(4): 236-240 (in Chinese) and PP-kurtosis in EV model. Mathematica Applicata. 2004. 17(1): Wu W B, Yao J H and Shen J W. Real-time long range transmission of 16-21 (in Chinese) log data through GPRS. Petroleum Instruments. 2005. 19(4): 72-73 Hew ett T A. Fractal distributions of reservoir heterogeneity and their (in Chinese) infl uence on fl uid transport. Society of Petroleum Engineers Annual Xia o L Z, Xie R H, Chai X Y, et al. Well logging technology for the Technical Conference and Exhibition. New Orleans, USA. 1986 new century: network-based logging technology. Well Logging Lia n F L, Moyne J R and Tilbury D M. Performance evaluation of Technology. 2003. 27(1): 6-10 (in Chinese) control networks: Ethernet, ControlNet, and DeviceNet. IEEE (Edited by Hao Jie)

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Published: Jul 23, 2009

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