Propagation effects of low frequency electromagnetic waves in production well

Petroleum Science, Jul 2012

The frequency domain electromagnetic method has already been widely used for tomographic imaging or electromagnetic well logging. However, different from open hole logging, the metal casing existing in production well logging has a strong shielding effect on the electromagnetic waves, thus bringing some difficulties to the application of the frequency domain electromagnetic method in production well logging. According to the relation of the field source geometry to the ring around the mandrel, the general expressions of frequency domain electromagnetic responses in axially symmetrical layered conductive medium are deduced. The propagation effects caused by the low-frequency electromagnetic waves in cased hole are also analyzed. The distribution curves of eddy current density and magnetic flux density along the radial direction in the mandrel indicate that the eddy loss within the mandrel is proportional to the transmission signal frequency and the mandrel conductivity. The secondary field responses of different casing materials show that the transmission frequency has an important effect on the ability of electromagnetic waves penetrating the metal casing. The transmission frequency should be ultra-low in order to enable the electromagnetic signal to penetrate the casing easily. The numerical results of frequency responses for different casing physical parameters show that the casing thickness has a significant impact on the choice of the transmission frequency. It is also found that the effect of the casing radius on the transmission frequency can be neglected.

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Propagation effects of low frequency electromagnetic waves in production well

Received May Propagation effects of low frequency electromagnetic waves in production well Song Xijin Guo Baolong Dang Ruirong Wang Xuelong The frequency domain electromagnetic method has already been widely used for tomographic bringing some difficulties to the application of the frequency domain electromagnetic method in layered conductive medium are deduced. The propagation effects caused by the low-frequency electromagnetic waves in cased hole are also analyzed. The distribution curves of eddy current density mandrel is proportional to the transmission signal frequency and the mandrel conductivity. The secondary on the ability of electromagnetic waves penetrating the metal casing. The transmission frequency should be ultra-low in order to enable the electromagnetic signal to penetrate the casing easily. The numerical results of frequency responses for different casing physical parameters show that the casing thickness casing radius on the transmission frequency can be neglected. response - 1 Introduction production capacity of wells is gradually decreasing and the water content is higher and higher. Therefore, the review and tapping of old wells is an essential complement to keeping the stability of oil and gas production. Moreover, it is also an effective way to enhance the overall effect of oilfield development. In view of the large number of cased developing through-casing resistivity characteristic al, 2004). Currently, through-casing resistivity logging has become an important means of monitoring old wells and the production process. In addition, the theory of cased hole formation resistivity logging and the calculation of apparent al, 2008a). In 1939, L. M. Alpin applied for the first patent about the formation resistivity measurement through casing in the United States. Since then, researchers in the United studying the measurement of formation resistivity through Logging successfully tested the first prototype of throughcasing resistivity logging according to the patent applied measurement theory based on the transmission line equation, which laid a solid foundation for through-casing resistivity In 1994, Schenkel and Morrison published a theoretical model based on integral equations, and discussed the logging a radial inhomogeneous medium (Schenkel and Morrison, 1994). The effects of casing thickness and cement sheath on the measurement results were also studied, which enriched and improved the basic theory of through-casing resistivity analyzed the characteristics of attenuation and phase shift of electromagnetic signals inside and outside the casing providing a theoretical basis for quantitative interpretation of the electromagnetic measurement through casing. The Schlumberger Company began to put the through-casing Resistivity) into commercial applications in 2000. In 2006, Russia also completed the development of a through-casing resistivity logging tool and actual measurements in the Liaohe 2010). logging, people pay relatively less attention to the electromagnetic logging in cased holes, mainly because the metal casing has a strong shielding effect on electromagnetic signals, and brings great difficulties to the transmitting and homogeneous medium may produce amplitude attenuation and refraction, i.e. propagation effects. Almost all highfrequency electromagnetic signals are absorbed by the casing and can not enter the formation, but some low-frequency electromagnetic signals can enter formation through the the low-frequency electromagnetic method in a borehole can identify the formation resistivity distribution by detecting the electromagnetic response in the receiver coil caused by eddy currents. Both the source and the receiver are located in the borehole, which makes the measuring device closer to the anomalous body. Therefore, the abnormal response signals are increased. The abnormal body can be detected in different heights and from each side. It can be used to study and study the distribution of remaining oil, and has a good characteristics of oil and gas production well, we derive logging response in a cylindrical layered medium, and analyze the propagation effects caused by the low-frequency electromagnetic waves in a multi-layer conductive medium. The electromagnetic response characteristics in the mandrel and formation are also discussed in detail. The results in this paper can provide an important theoretical basis for the forward modeling, inversion and interpretation of lowfrequency electromagnetic logging in production wells. 2 Field equations and their solutions Low frequency electromagnetic logging methods in production wells use a coil around a mandrel as the source. T and the receiving coil R are around a mandrel in borehole. The vertical offset between the two coils is z. Mandrel, hole, casing and formation have conductivity { 1, 2 , 3 , 4}, permittivity { 1, 2, 3, 4} and permeability { 1, 2, 3, 4}. There are three cylindrical interfaces in cylindrical layered casing. Their outer-radii are r, r1 and r2, respectively. The basic principle of low-frequency electromagnetic method in apply low frequency alternating current to the transmitting coil, the electromagnetic field caused by the current would enter the formation though the casing, and produce eddy So we can determine the formation resistivity characteristics of time-domain electromagnetic logging in boreholes previously (Song et al, 2011). The results indicated that compared with metal casing, the impact of a cement sheath on electromagnetic signals is small, and can be neglected especially for low resistance formation. Therefore, in order cement sheath. R Z T r 1 r1 r2 2 3 4 2.1 Field of conductive homogeneous medium To solve the boundary value problems of electromagnetic solution items of the non-homogeneous wave equation in the active region. This particular solution is the primary source geometry of the ring current source (transmitting coil) z=z0 in the 0. So the physical model 0 . The field i i I 0 I ( 1 I 0 K ( 1 0 ) ( 0 ) ( dA 0 0 ) 0 ) dAe 0 0, the total magnetic 0 of an infinite number of fields produced by the electric r0=( 0, 0), and the current source with an arc length of dl is an electric dipole. Then the electric dipole source is perpendicular to the meridian plane of the azimuth 0, and points to the direction e 0 I=I0e to the ring current source, where, g where, (r) is the Dirac function. In cylindrical coordinates, the magnetic vector potential components in the azimuth direction e are given by: z z has a component only in direction , that is: 0 )K1( ) cos (z )K1( 0 ) cos (z z0 )d z0 )d ( ( 0 ) 0 ) gK1 ( gI1( ) cos (z z0 ) ( ) cos (z z0 ) ( 0 ) 0 ) (1) (2) (3) (5) (6) (7) 0 (8) (9) (10) 2.2 Field in a layered lossy medium . So the secondary electric field in a layered medium also only has a component in direction , which meets the passive the general solution only has the secondary field response. Therefore, the electric field responses in a four layered medium are as follows: z z z z B K z z A I z z By the relationship of the magnetic potential vector and the By Eqs. (12) and (14), we can obtain the vertical magnetic 3 Analysis of propagation effects T h e p r o p a g a t i o n o f e l e c t r o m a g n e t i c w a v e s i n a of the incident wave vector ki, reflected wave vector kr and transmitted wave vector kt are shown in Fig. 3, where n is the (18) rTE where, refraction. For the condition of two interfaces, the propagation of electromagnetic waves is shown in Fig. 4. It can be seen reaches the second interface, reaches the first interface, it becomes the incident wave A1, A2, A3 borehole and casing, respectively, and B2, B3, B4 represent of the tangential component of the electric and magnetic 4 Numerical calculation of propagation effects 4.1 Eddy current loss within the mandrel 1, 1, 1 exist within the mandrel, the attenuation characteristics of depth 2 . For different r/ 1 1 of J/J0 and B/B0 changing with /r inside the mandrel. J0 and B0 the mandrel surface. r is the mandrel radius and is the radial r is fixed, the higher the transmitted within mandrel is more serious. This result indicates that the and 1 r, the smaller . The distribution proportional to the mandrel radius. 4.2 Field within the mandrel offset between two coils z 0 J / J 0 B / B 1 -1 -0.5 represents the real part of the electric field response within the mandrel, Fig. 6(b) represents the real part of the magnetic part of the magnetic field response. The simulation results show that the electromagnetic responses within the mandrel higher the amplitude of the electromagnetic field response magnetic field lines within the mandrel reduces with the electromagnetic response amplitude. Next, we discuss the impact of mandrel radius on its internal electromagnetic response. We take the mandrel radius r 2 3 Mandrel conductivity, S/m (a) 4×106 1 2 3 Mandrel conductivity, S/m 4 ×106 (b) 4 3 m /A 2 , 1 z lH 1 a e R 0 -1 ×10-5 1 ×10-5 /m0 A , 1 z H g a -1 m I -2 1 radii are shown in Fig. 7. For a larger mandrel radius, the electromagnetic field responses within it become lower. 4.3 Field in the formation 2 3 Mandrel conductivity, S/m (d) conductor has a serious shielding effect on electromagnetic the casing material is fixed. We choose iron ( 7 S/m, r =1000), aluminum ( 7 S/m, r =1), copper ( 7 S/m, r =1), and nickel ( 7 S/m, r materials. Fig. 8(a) shows the real part of the electric field 1 =2,000,000 S/m, Fig. 8(b) shows the real part of the electric 1 =4,000,000 S/m and Fig. 8(c) shows 1 =6,000,000. a cased hole. For the metal casing, the lower the transmission depth in the casing must be greater than the casing thickness. 3 k3 i i reflection coefficient at the inner casing can be obtained rTE 1 shielding effect on electromagnetic signals. Furthermore, for the cased hole, the peak of the electric field response f 1 2 3 4 Mandrel conductivity, S/m 2 3 4 Mandrel conductivity, S/m borehole is uncased, this peak is f with Fig. 9(b) and Fig. 9(c) or comparing Fig. 9(d) with Fig. response amplitudes in the formation reduce with an increase weaker the electromagnetic signals in the formation. weaker the electromagnetic signals penetrating casing. We select iron, aluminum, copper, and nickel as the casing casing materials are shown in Fig. 9. Fig. 9(a) shows the 1r = 200, Fig. 9(b) shows the real part of the electric field response when 1r = 300 when 1r = 400. Fig. 9(d), Fig. 9(e) and Fig. 9(f) correspond parameters on the response signals in the formation. The r = r2 r1=3, 6, 9, 11 mm, of different casing thickness. The simulation results show that the thicker the casing, the lower the response signal penetrating the casing with an increase of transmission r = 3 mm, the peak is corresponding to the transmission r = 11 mm, the peak is casing thickness in order to make the electromagnetic signals 1=2000000 S/m ×10-10 -1010-2 -610-2 102 -210-2 100 10-2 ×10-10 m / V , 4 E g a m I m / V , 4 E l a e R m / V , 4 E g a m I 15 10 5 0 -5 10-2 1 0 -1 -2 ×10-9 ×10-9 10-2 2 1 0 -1 10 -2 m / A , 4 z H l a e R m / A , 4 z H g a m I ×10-4 10-2 ×10-4 m / A , 4 z H-2 l a e R -4 -6 2 0 4 5 ½ inch casing 7 inch casing 100 Frequency, Hz We also compute the electromagnetic responses of different casing diameters are shown in Fig. 11. The figure shows that when the casing thickness remains unchanged, the larger the casing diameter, the higher the response signal amplitudes. This phenomenon can be interpreted as the casing field lines. The decrease of magnetic field lines entering the formation resulting in a decrease of signal response amplitudes. So we can infer that as long as the casing thickness remains unchanged, the skin depth required for the electromagnetic signal penetrating the casing is the same, and 5 Conclusions amplitude attenuation and phase shift, but also reflection electromagnetic logging methods in a production well. The general expressions of electromagnetic response in a uniform medium are also discussed in detail. The simulation results 2008a. 51(Supp 1747 5(2): 126-134 Shen J S and Sun W B. 2.5-D modeling of cross-hole electromagnetic influence upon the electromagnetic responses within the the casing thickness has an important impact on the selection 1991 that the effect of the casing diameter can be ignored. The geological formation from within cased well in presence of acoustic cased well while passing electrical current between two cased well. Vail W B. Methods of operation of apparatus measuring formation method. Acknowledgements Science. 2009 . 6 ( 3 ): 225 - 229


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Xijin Song, Baolong Guo, Ruirong Dang, Xuelong Wang. Propagation effects of low frequency electromagnetic waves in production well, Petroleum Science, 2012, 182-191, DOI: 10.1007/s12182-012-0198-5