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1 easuring orizontal Resistivity R in orizontal Well Logging Downloaded 5//16 to Redistribution subject to SEG license or copyright; see Terms of Use at T. agiwara Terry Research and Development and Shell International Exploration and Production Summary In horizontal wells, the conventional coaxial induction tool response is determined by both the horizontal conductivity σ and the vertical conductivity σ V. With the coaxial LWD induction-type tools operating at z and 4 kz, the horizontal conductivity σ and the anisotropy a, hence the vertical conductivity σ V, can be measured simultaneously from two independent coaxial measurements (such as the phase resistivity and the attenuation resistivity). The WL coaxial induction tools operating at lower frequency around kz measures the geometric average of horizontal and vertical conductivities σ σ V in horizontal wells if only the in-phase signal is used. If a tri-axial induction tool is used, two additional resistivity measurements are available from two coplanar responses in horizontal wells. Vertical coplanar response is determined only by the horizontal conductivity σ in horizontal well logging, where both transmitter coil and receiver coil are oriented vertically and perpendicularly to the horizontal tool axis. orizontal coplanar response is determined by both horizontal conductivity σ and vertical conductivity σ V where both transmitter and receiver antennas are oriented horizontally and perpendicularly to the tool axis. But at low (induction log) frequency, the horizontal coplanar response is also determined nearly by horizontal conductivity σ alone. Introduction Log interpretation in horizontal wells is not simple. The geometry can be no longer axial symmetric around logging tools and the D geometry have to be taken into consideration to interpret the response of logging tools. Even if the effect of D geometry is ignored, the data collected in horizontal wells may not be the same as in vertical wells, if the data concern the directional measurement such as the electric resistivity and the fluid permeability of a formation. Consider electric resistivity data. any of core resistivity measurements are made on the horizontal resistivity on horizontal plugs from the cores taken in vertical wells (agiwara 1986). Tying wells are based on the horizontal resistivity measured in vertical wells. Shale resistivity trend curves are based also on the horizontal shale resistivity in vertical wells. Therefore, it is particularly important to obtain the horizontal resistivity in horizontal well logging. Conventional induction tools and induction-type LWD resistivity tools are coaxial tools where both the transmitter and receiver coils are wound around the tool axis. It has been shown that the coaxial tool measures the horizontal resistivity R in vertical wells. Galvanic resistivity tools such as Normal log and Laterolog also measure resistivity very closely to the horizontal resistivity in vertical wells (oran and Gianzero). The small difference between the Laterolog resistivity and the coaxial induction log resistivity depends on the resistivity anisotropy (Chemali et al., agiwara and Zea 1999). In horizontal wells, the coaxial induction tool response is determined by both horizontal conductivity σ and vertical conductivity σ V. With the coaxial LWD induction-type tools operating at z and 4 kz, the horizontal conductivity σ and the anisotropy a, hence the vertical conductivity σ V, can be measured simultaneously from two independent coaxial measurements (such as the phase resistivity and the attenuation resistivity). The WL coaxial induction tools operating at lower frequency around kz measures the geometric average of horizontal and vertical conductivities σ σv in horizontal logging if only the in-phase signal is used. As for a tri-axial induction tool, vertical coplanar response is determined only by horizontal conductivity σ in horizontal well logging, where both transmitter coil and receiver coil are oriented vertically and perpendicularly to the horizontal tool axis. orizontal coplanar response is determined by both the horizontal conductivity σ and the vertical conductivity σ V where both the transmitter and the receiver antennas are oriented horizontally and perpendicularly to the tool axis. But at low (induction log) frequency, the horizontal coplanar response is also determined by ther horizontal conductivity σ alone. Theory SEG/New Orleans 6 Annual eeting 1786

2 easuring orizontal Resistivity R in Downloaded 5//16 to Redistribution subject to SEG license or copyright; see Terms of Use at Conventional induction-type resistivity tool is called a coaxial tool in which both the transmitter and the receiver loop antenna are wound around the tool axis. As for a triaxial induction tool, there are three other measurements that are non-vanishing in homogeneous formations, in addition to the coaxial response: they are they are coplanar, cross-component, and Yy-coplanar responses. They are shown in Fig.1. Figure 1. Antenna configuration of induction-type tool It has been shown that the magnetic field strength vector measured with induction-type resistivity tools in a homogeneous anisotropic formation is given by (agiwara 4), ik L ik L ik Lβ = coaxial (1 ik e + ik L e e [ 1 ik L + ( ik ] ik L e = coplanar cos θ + ik L ik Lβ ik L e e sin θ θ ik = cos cross component ik L e sinθ L ik e Lβ [ ik L 1 ik ] L + ( ik e ik L ik Lβ = 1 Yy coplanar ik L e e sin θ ik L α ik Lβ + ( ik e e β Zy = Xy = Yz = Yx = where the formation is specified by the horizontal conductivity σ and the vertical conductivity σ V, and k σ iωµ σ. V R α = = is the anisotropy, and σ R V β = 1 = ( α 1) sin θ. is the effective magnetic dipole moment of the transmitter loop antenna. L is the spacing between a transmitter and a receiver, and θ is the effective dip (deviation) angle between the tool axis and the vertical direction of the formation. Resistivity measurements in vertical wells In vertical wells, θ = and β=1, regardless to anisotropy. The response of conventional coaxial tools is determined only by the horizontal conductivity σ as, ik L coaxial = { ( 1 ik e } Namely, conventional coaxial tools measure the horizontal conductivity σ in vertical wells. Cross-component response is zero in vertical wells. Two coplanar tool responses are identical in vertical wells and in general depend on both the horizontal and the vertical conductivity, as, coplanar = Yy coplananr + = α 1 ik L 1 ik L + ( ik e At very low frequency, the coplanar tools would measure the vertical conductivity σ V as, coplanar = Yy coplananr α +... = 1 1 i ωµ +... σ L 1 i ωµ σv L πl πl in contrast to = ik coaxial ( 1 ik ) L e 1 i ωµ σ L +... πl { L}. SEG/New Orleans 6 Annual eeting 1787

3 easuring orizontal Resistivity R in Downloaded 5//16 to Redistribution subject to SEG license or copyright; see Terms of Use at owever, in-phase coplanar response still depends on the anisotropy at induction log frequency of kz, as shown in Fig.. Figure. Coplanar response in vertical wells Resistivity measurements in horizontal wells with conventional coaxial tools In horizontal wells, θ =π/ and β=α= (σ V /σ ). The response of conventional coaxial tools is determined by both the horizontal conductivity σ and the anisotropy α (or the vertical conductivity σ V =σ α ). ik L ik Lα coaxial = {( ik e ( ik e } Conversely, in horizontal wells, both the horizontal conductivity σ and the anisotropy α (or the vertical conductivity σ V =σ α ) can be measured from two independent coaxial responses, such as in-phase and outphase amplitude at induction log frequency, or the phase and the attenuation resistivity at LWD frequency. Fig. shows a nomogram to determine both the horizontal resistivity R and the anisotropy α from the phase resistivity R5P and the attenuation resistivity R5A of 5 spacing z LWD induction-type tool (agiwara 1996). Figure. A nomogram to determine R and anisotropy Resistivity measurements in horizontal wells with a triaxial induction tool Cross-component response is zero in horizontal wells. A tri-axial induction tool has two non-vanishing coplanar measurements in a homogeneous anisotropic formation, in addition to the conventional coaxial measurement. One coplanar measurement is between the transmitter and receiver loop antennas both of which are perpendicular to the tool axis (horizontal well) and vertical. {[ ik L coplanar = 1 ik L + ( ik ] e } This vertical coplanar response is determined only by k, namely by the horizontal conductivity σ. Conversely, the coplanar tool measures the horizontal resistivity. The Yy-coplanar measurement is between the pair of transmitter and receiver both of which are perpendicular to the tool axis and horizontal. This horizontal coplanar response is determined by both horizontal conductivity and anisotropy. ik L ik Lα Yy coplanar = { e ik L [ ik Lα] e 1 } ( ) Just like with the coaxial measurement, both the horizontal conductivity σ and the anisotropy α (or the vertical conductivity σ V =σ α ) can be measured simultaneously from two independent horizontal Yy-coplanar responses. Or, they can be measured from a combination of coaxial and coplanar, vertical or horizontal, responses. At very low frequency, while coaxial tool measures geometric average of σ andσ V, as 1 coaxial i ωµ σ +... L α πl = 1 i ωµ σ L +... σv πl while the both vertical and horizontal coplanar tools would measure the horizontal conductivity σ as, = 1 coplanar Yy coplananr 1 i ωµ σ L L π Even at induction log frequency of kz, this is a very good approximation for both the coaxial and the horizontal Yy-coplanar measurements, as shown in Fig.4 and Fig.5, respectively. SEG/New Orleans 6 Annual eeting 1788

4 easuring orizontal Resistivity R in from a combination of coaxial and coplanar responses. At low induction frequency, both vertical and horizontal (Yy-)coplanar responses measures the horizontal conductivity Downloaded 5//16 to Redistribution subject to SEG license or copyright; see Terms of Use at Conclusion In horizontal well, conventional induction-type coaxial tool response is determined by both the horizontal conductivity and the vertical conductivity. With the conventional coaxial tool in horizontal wells, the horizontal conductivity σ and the anisotropy α (hence the vertical conductivity σ V ) can be measured from two independent coaxial measurements, such as the phase and the attenuation resistivity of LWD resistivity tools. With a tri-axial induction tool in horizontal well, the horizontal conductivity is measured by the vertical coplanar response alone. The horizontal Yy-coplanar response is determined by both the horizontal conductivity and the vertical conductivity in horizontal wells, similarly to the coaxial response. The horizontal conductivity σ and the anisotropy α (hence the vertical conductivity σ V ) can be measured from two independent Yy-coplanar measurements, or Acknowledgement The author is grateful for Shell International Exploration and Production Company for permitting the publication of this work. References Chemali R, Gianzero S and Su S (1987) The effect of shale anisotropy on focused resistivity devices, Paper, Transactions of the SPWLA 8th Annual Symposium, London, England, June 9-July. T. agiwara (1986), On the Direction of Core Dielectric Constant and Conductivity easurements, Log Analyst, November-December, p.6 T.agiwara (1996), A New ethod to Determine orizontal Resistivity in Anisotropic Formation without Prior Knowledge of Relative Dip, Paper Q, Transactions of the SPWLA 7th Annual Symposium, New Orleans, LA, June T.agiwara (4), ethod for determining anisotropic resistivity and dip angle in an earth formation, US 6,76,666, July 6 T.agiwara and. Zea (1999), Identifying and Quantifying Resistivity Anisotropy in Vertical Boreholes, paper ZZ, Transactions of the 4th SPWLA Annual Symposium, Oslo, Norway, June oran, J.. and Gianzero, S. (1988), Effects of formation anisotropy on resistivity measurements, Geophysics vol.4, p SEG/New Orleans 6 Annual eeting 1789

5 Downloaded 5//16 to Redistribution subject to SEG license or copyright; see Terms of Use at EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 6 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES Chemali, R., S. Gianzero, and S.. Su, 1987, The effect of shale anisotropy on focused resistivity devices: 8th Annual Symposium, SPWLA, Paper. agiwara, T., 1986, On the Direction of Core Dielectric Constant and Conductivity easurements, Log Analyst, 6., 1996, A new method to determine horizontal resistivity in anisotropic formation without prior knowledge of relative dip: 7th Annual Symposium, SPWLA, Paper Q., 4, ethod for determining anisotropic resistivity and dip angle in an earth formation: U. S. Patent agiwara, T., and. Zea, 1999, Identifying and Quantifying Resistivity Anisotropy in Vertical Boreholes: 4th Annual Symposium, SPWLA, Paper ZZ. oran, J.., and S. Gianzero, 1988, Effects of formation anisotropy on resistivity measurements: Geophysics, 4, SEG/New Orleans 6 Annual eeting 179