Luis E. San Martin

Three-dimensional simulation of eccentric LWD tool response in boreholes through dipping formations

We simulate the response of logging-while-drilling (LWD) tools in complex thee-dimensional (3-D) borehole environments using a finite-difference time-domain (FDTD) scheme in cylindrical coordinates. Several techniques are applied to the FDTD algorithm to improve the computational efficiency and the modeling accuracy of more arbitrary geometries/media in well-logging problems: (1) a 3-D FDTD cylindrical grid to avoid staircasing discretization errors in the transmitter, receiver, and mandrel geometries; (2) an anisotropic-medium (unsplit) perfectly matched layer (PML) absorbing boundary condition in cylindrical coordinates is applied to the FDTD algorithm, leading to more compact grids and reduced memory requirements; (3) a simple and efficient algorithm is employed to extract frequency-domain data (phase and amplitude) from early-time FDTD data; (4) permittivity scaling is applied to overcome the Courant limit of FDTD and allow faster simulations of lower frequency tool; and (5) two locally conformal FDTD (LC-FDTD) techniques are applied to better simulate the response of logging tools in eccentric boreholes. We validate the FDTD results against the numerical mode matching method for problems where the latter is applicable, and against pseudoanalytical results for eccentric borehole problems. The comparisons show very good agreement. Results from 3-D borehole problems involving eccentric tools and dipping beds simultaneously are also included to demonstrate the robustness of the method.

Numerical Modeling of Eccentered LWD Borehole Sensors in Dipping and Fully Anisotropic Earth Formations

Logging-while-drilling (LWD) borehole sensors are used to provide real-time resistivity data of adjacent earth formations for hydrocarbon exploration. This allows for a proactive adjustment of the dipping angle and azimuth direction of the drill and, hence, geosteering capabilities. The analysis of borehole eccentricity effects on LWD sensor response in full 3 3 anisotropic earth formations is important for correct data interpretation in deviated or horizontal wells. In this paper, we present a cylindrical-grid finite-difference time-domain model to tackle this problem. The grid is aligned to the sensor axis to avoid staircasing error in the sensor geometry but, in general, misaligned to the (eccentered) borehole/formation interface. A locally conformal discretization is used to compute effective conductivity tensors of partially-filled grid cells at those interfaces, involving an isotropic medium (borehole) and a full 3 3 anisotropic medium in general (dipped earth formation). The numerical model is used to compute the response of eccentered LWD sensors in layered earth formations with anisotropic dipping beds.

Modeling of EM logging tools in arbitrary 3-D borehole geometries using PML-FDTD

We discuss the numerical modeling of logging-while-drilling (LWD) tools for hydrocarbon exploration in arbitrary three-dimensional geometries using a new finite-difference time-domain (FDTD) scheme in cylindrical coordinates. Two locally conformal FDTD (LC-FDTD) schemes are employed to simulate eccentric LWD tools in realistic logging environments. An anisotropic perfectly matched layer absorbing boundary condition extended to cylindrical coordinates is incorporated in the FDTD method to simulate unbounded geophysical formations. Frequency-domain data are obtained from the time-domain results using a ramp-modulated sinusoidal source and an efficient early-time extraction algorithm. The FDTD simulations are validated against both numerical mode matching and pseudoanalytical approaches and show very good agreement.

Integration of 3D Modeling and Real-time Processing for Enhancement of Anisotropic Formation Evaluation with Borehole Multicomponent Induction Measurements

It is well known that around the world a number of oil and gas reservoirs consist of formations which are identified as resistivity/conductivity anisotropic by borehole induction tools, such as thinly laminated sand-shale or bedded sand-sand rock sequences. Therefore, resistivity-anisotropy formation properties are critical for accurately evaluating anisotropic reservoirs. For many years the logging industry has tried to use induction tools to measure both horizontal and vertical resistivities of reservoir formations. As one of the latest and most remarkable developments in the wireline induction logging domain, multicomponent induction (MCI) logging is now used to fill this requirement. Compared to conventional induction, this new logging technology is able to measure the formation anisotropy (vertical and horizontal resistivities, Rv and Rh, respectively), dip, and strike required to accurately evaluate different types of anisotropic reservoirs. When interpreting MCI data for the purpose of anisotropic formation evaluation, most cases theoretically require 3D electromagnetic (EM) forward modeling and inversion. However, experience has clearly shown that the current 3D forward modeling algorithms often fail to obtain accurate solutions in a reasonable amount of CPU processing time. Even for the most efficient algorithms, fully 3D inversion is impractical for the real-time or well-site delivery of inverted results from measurements. For fast and accurate 3D EM forward modeling, a practical 3DFD (finite difference) method based on an isotropic/transverse isotropic (TI) background is presented and used. This method has been tested by fast borehole-effect correction (BHC) and several independent 3D codes. Its practical application workflow is also proposed and tested. The timeconsuming 3D inversion is generally partitioned into a few simple and fast data processes including resolution enhancement of MCI logs for reducing shoulder-bed effects and a few low-dimensional inversions such as radially one-dimensional (R1D) inversion, which makes possible the real-time delivery of formation anisotropy (Rh and Rv), dip, and strike information. Moreover, the R1D inversion is based on a fast and rigorous multistep inversion algorithm and a fast forward modeling engine which consists of the pre-calculated MCI-response library created by using the fast 3DFD method. This novel method of integrating 3DFD numerical modeling and real-time processing technologies has been proposed and implemented for enhancing anisotropic formation evaluation. To demonstrate its capability and effectiveness, we successfully validated the method on both synthetic data and field log data sets.