Inversion of well data using vertical electrodes with time domain acquisition

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An inversion method that uses the vertical electric field from a vertical electric dipole has been developed. The inversion method is based on Marquardt-Levenberg’s scheme and forward modeling, iterating over layers with different resistivity. An
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    Introduction An offshore, time domain EM method that uses vertical, stationarytransmitters and receivers has been developed by the Norwegiangeophysical company Petromarker (Holten et. al, 2009). Receiver datafrom short offsets in the range of 500 to 1500 m are used to probe theelectrical near-field that results from turning off a source current. Thevertical electrical field is sensitive to deep resistive layers, and the modelingshows a significant difference between a hydrocarbon-filled and a waterfilled reservoir. A traditional controlled source electromagnetic (CSEM)technology that is based on a horizontal transmitter-horizontal receiversetup, measures a large EM direct wave (reflected from sea surface), and asmaller signal from the underlying rock. We demonstrate the ability of thisCSEM method using vertical dipoles and antennas for detecting ahydrocarbon layer. Data are extracted from the composite log of wellbore34/8-1 (Visund) in the North Sea, and then blocked in intervals to constructthe resistivity model. The forward modelling is performed based on theresistivity model and the inversion of the forward model with added noise isin good agreement with the srcinal resistivity model. Forward Modelling   We investigate a synthetic case with an upscaled resistivity log. The datafrom the composite log of the well 34/8-1 (Visund field) in the North Sea isdivided into small vertical intervals, 100 m layers outside the reservoir and10 m layers inside the reservoir. A resistivity model is constructed and weused the algorithm created by Petromarker to create a forward model. Thewater depth in the prospect area is 326 m, the reservoir depth is 2767 m,reservoir th ickness is 97 m and the average reservoir resistivity is 204 Ωm  A background reference model was made where the reservoir resistivity isset to the background value (Fig. 3). Two electric field responses arecalculated, E 0 (t) for the background case and E HC (t), for a model whichincludes the resistive hydrocarbon layer. We also estimate the anomalousvertical field E A =E 0 (t)-E HC (t), and the contrast S=1-E HC (t)/E 0 (t). Often thecontrast is as important as the anomaly itself. The anomaly is largelydetermined by the transverse resistivity = (thickness * resistivity) of theoverburden compared to the transverse resistivity of the reservoir. Theresult of the forward model is shown in Fig. 4. Inversion A 1D inversion algorithm has been developed by Petromarker which isbased on Marquardt- Levenberg’s and Occam numerical techniques. A reasonable amount of noise is added to the output data from the forwardmodel (corresponding to the measured data or response) which can beinverted. The ill-posed inversion problem can be solved by introducingpriori information about unknown parameters. Priori information isincorporated to the inverse problem by constraining electrical conductivityand layers thickness.In resistivity well logs, there are often variations within a few meters. Thesewell logs are used to extrapolate resistivity data to other locations and toupscale the logs to a more convenient vertical grid size. This leads touncertainties, which can be modelled by creating a set of forward modelswith resistivities which are drawn from the well log. Random noise can beadded to the response curves to emulate measurement noise and then theresults can be inverted and compared to the srcinal model. This methodcan evaluate the robustness of the inversion, and be used with geologicaldata to calculate the chance of finding hydrocarbon.We have added noise to the HC-response curve in Figure 4, and invertedthe result (Figure 5). The corresponding resistivity models are shown infigure 6. As expected, as noise is added, the response curves and resistivitymodel differs more from the initial model. With 50-100 nV of added noise,the inversion can no longer find the HC layer. Conclusions An inversion method that uses the vertical electric field from a verticalelectric dipole has been developed. The inversion method is based onMarquardt- Levenberg’s scheme and forward modeling, iterating over layers with different resistivity.An example from the North Sea is shown where the hydrocarbon layer isdiscernable after adding a realistic noise level to a forward model. Theresistivity model of the Visund field (wellbore 34/8-1) was constructedfrom the composite log. The forward model is done by using our algorithm,and the observable contrast of the model is 78%. There is a good agreementof the inversion results and the srcinal resistivity model, indicating that ourtechnology is able to detect this HC layer. Inversion of well data using vertical electrodes with timedomain acquisition Terje Holten 1  Abdul Wahab El Kaffas 1,2  Eirik Grude Flekkøy 1,3   1 Petromarker, Stavanger, Norway 2 Department of physics, University of Suez Canal 3 Department of physics, University of Oslo Fig. 1 Petromarker Technology setup Drilling operator: Statoil Petroleum ASArea: North Sea (NCS)Discovery: 34/8-1 VisundWellbore contents: Oil/GasWater depth 326 mReservoir depth, Thickness: 2767, 97 mReservoir resistivity: 204 Ωm  Observable contrast:77% Fig. 2   Well 34/8-1 (Visund field)   Fig. 5 Forward Model with noiseFig. 6 Inversion of synthetic data   Fig. 3 Blocked data of wellFig. 4 Comparing water and HC filled reservoirs
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