Simulation of DC dual-laterolog measurements in complex formations: A Fourier-series approach with nonorthogonal coordinates and self-adapting finite elements

Abstract

Dual laterolog (DLL) makes use of a galvanic conduction principle to focus electrical currents into rock formations, thereby minimizing shoulder and borehole effects in the measurement of formation resistivity. The tool includes two separate focusing systems: deep-sensing (LLd) and shallow-sensing modes (LLs). Laterolog current-focusing systems were designed for operation primarily in vertical boreholes penetrating horizontal layers; only recently their design has been revised for operation in deviated wells in the presence of electrical anisotropy. We simulated three-dimensional (3D) DLL measurements in dipping, invaded, and electrically anisotropic formations and appraised the corresponding effects on apparent resistivity logs. Simulations were performed by combining the use of a Fourier-series expansion in a nonorthogonal system of coordinates with an existing 2D goal-oriented, higher-order, and self-adaptive finite-element method. This numerical algorithm yields accurate solutions in limited CPU time because only a few Fourier modes are needed to simulate practical applications. For the calculation of focused currents, we introduced an embedded postprocessing method that incorporates a synthetic focusing principle to compute current intensities at each iterative step of optimal mesh refinements. Our numerical method accurately simulates 3D DLL measurements in rock formations that exhibit extreme contrasts of electrical resistivity. Simulations indicate that LLs resistivity logs are more sensitive to both invaded and anisotropic layers than LLd resistivity logs. In deviated wells, shoulder-bed effects on apparent resistivity logs increase with an increase of dip angle, and are emphasized across thin conductive layers. Electrical anisotropy effects on apparent resistivity logs increase substantially with dip angle.

Analyzing the Origin of Low Resistivity in Gas-Bearing Tight Sandstone Reservoir

“…The simulated mud invasion time was 7 d, considering that the time from drilling to logging is approximately 7 d, and the invasion depth and invasion zone resistivity were obtained. The finite element forward model [38,39] was applied to calculate the array lateralog responses of the simulation area [40][41][42]. In Figure 12, the fifth track is the comparison between the measured and simulated value of array lateralog responses.…”

Assessment of Delaware and Groningen effects on dual-laterolog measurements with a self-adaptive hp finite-element method

“…In LLd mode, all bucking current electrodes inject current and all of the injected currents return to the current-return electrode ͑B͒ at the earth's surface, which can be easily 2 to 3 km apart from the logging point. The two focusing systems of DLL instruments provide different current paths ͑Figure 1͒ and radial lengths of investigation ͑Anderson, 2001; Cozzolino and Silva, 2007;Nam et al, 2009͒. Service companies have been manufacturing DLL tools to work in slightly different ways, possibly with different focusing ͑or monitoring͒ conditions and different dimensions ͑e.g., Anderson, 2001;Cozzolino and Silva, 2007;Yang et al, 2007;Nam et al, 2009͒. In this study, we implement a specific commercial DLL tool configuration ͑Figure 1͒ whereby we place each simulated electrode at the same location and with the same vertical dimension as that of the commercial DLL tool. We assume that the resistivity of all of the electrodes is 10 ‫5מ‬ ohm-m, whereas the resistivity of the tool's mandrel is 10 5 ohm-m, resulting in a resistivity contrast at the interfaces between electrodes and insulator equal to 10 10 .…”

“…Most DC simulations of DLL measurements reported to date ͑e.g., Liu et al, 1999;Cozzolino and Silva, 2007;Nam et al, 2009͒ assumed the following two operating conditions: ͑1͒ electrode B is at infinity, and ͑2͒ electrode N is at zero potential ͑Anderson, 2001͒. Under extreme logging conditions, these simulation assumptions become inadequate and, hence, fail to simulate Delaware effects accurately.…”

“…The algorithm uses a 2D goaloriented, higher order, self-adaptive hp finite-element ͑FE͒ method ͑Pardo et al, 2006;Pardo et al, 2007͒ ͑h denotes the element size and p the polynomial order of approximation within each element͒ and uses an embedded postprocessing method ͑EPPM; Nam et al, 2009͒ for the calculation of focused currents. EPPM incorporates a synthetic focusing principle to compute current intensities at each iterative step of optimal mesh refinements.…”