Xinding Fang

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ∼27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d0. The optimal parameter space for the maximum value of the linear frequency-shifted factor (α0) and the scaling factor (β0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.

Sequential approach to joint flow‐seismic inversion for improved characterization of fractured media

Seismic interpretation of subsurface structures is traditionally performed without any account of flow behavior. Here we present a methodology for characterizing fractured geologic reservoirs by integrating flow and seismic data. The key element of the proposed approach is the identification—within the inversion—of the intimate relation between fracture compliance and fracture transmissivity, which determine the acoustic and flow responses of a fractured reservoir, respectively. Owing to the strong (but highly uncertain) dependence of fracture transmissivity on fracture compliance, the modeled flow response in a fractured reservoir is highly sensitive to the geophysical interpretation. By means of synthetic models, we show that by incorporating flow data (well pressures and tracer breakthrough curves) into the inversion workflow, we can simultaneously reduce the error in the seismic interpretation and improve predictions of the reservoir flow dynamics. While the inversion results are robust with respect to noise in the data for this synthetic example, the applicability of the methodology remains to be tested for more complex synthetic models and field cases.

Double-beam stacking to infer seismic properties of fractured reservoirs

Summary We develop a theory for using 3D beam interference to infer scattering properties of a fractured reservoir using reflected seismic P data. For the sake of simplicity, we use Gaussian beams. The scattering properties are important to infer fracture spacing, orientation and compliance. The method involves the interference of two beams, one from the source region and the other from the receiver region. Each beam is formed by first windowing the data in space and time and then performing f-k filtering. The interference pattern depends on frequency, the incident angle, the reflection angle, and the azimuth. We try to interpret the interference pattern using local Born scattering in the target region. This interpretation is motivated by the observation that full-wave finite difference simulation of waves propagating through a set of vertical fractures using Schoenberg’s linear-slip boundary condition and fracture compliances consistent with those inferred from field and laboratory data shows that single scattering dominates in the reflection data. The methodology is versatile in that by adjusting the window sizes we can obtain plane wave interference as well as interference for a single shot or receiver gather. By suitable choice of pairs of source and receiver beams, the spatially varying fracture properties as well as the fracture orientation can be inferred.

On perfectly matched layer schemes in finite difference simulations of acoustic Logging‐While‐Drilling

In the wave propagation simulation by finite difference time domain (FDTD), the perfectly matched layer (PML) is often applied to eliminate the reflection artifacts due to the truncation of the finite computational domain. In the acoustic Logging-While-Drilling (LWD) FDTD simulation, due to high impedance contrast between the drill collar and fluid in the borehole, the stability and efficiency of PML scheme is critical to simulate complicated wave modes accurately. In this paper, we compare four different PML implementations in FDTD in the acoustic LWD simulation, including splitting PML (SPML), Multi-axis PML (MPML), Non-splitting PML (NPML), and complex frequencyshifted PML (CFS-PML). The simulation indicates that NPML and CFS-PML can more efficiently absorb the guide wave reflection from the computational boundaries than SPML and MPML. For large simulation time, SPML, MPML and NPML are numerically instable. However, stability of MPML can be improved further to some extent. Among all, CFS-PML is the best choice for LWD modeling. The effects of CFS-PML parameters on the absorbing efficiency are investigated, including damping profile, frequency-shifted factor, scaling factor and PML thickness. For a typical LWD case, the best value for maximum of quadratic damping profile d0 is about 1. The optimal parameter space for the maximum value of linear frequency-shifted factor α0 and scaling factor β0 depends on the PML damping profile and thickness. If the PML thickness is 10 grids, the reflection residual can be reduced to less than 1%, using optimal CFS-PML parameters, while only about 0.5‰ reflection artifacts are observed for 20 grids PML buffer.

Full elastic finite-difference modeling and interpretation of karst system in a subsalt carbonate reservoir

AbstractWe evaluated an advanced forward-modeling-based reservoir characterization technique that uses full elastic finite-difference simulation to investigate the limits of karst identification in stacked seismic data. Identification of karsts is important for field development in carbonated reservoirs because paleokarst features can result in a loss of circulation and/or sometimes lost drill bits. Our primary objective was to verify whether we can detect and interpret the location and size of karsts from seismic data, especially given a complex overburden. We constructed an elastic reservoir model consisting of compressional velocity (VP), shear velocity (VS), and density for the study area using interpreted horizons and well log information. Karsts with varying widths, thicknesses, dip angles, and porosities were inserted to generate multiple versions of the model. We also evaluated the imaging impact of overlying faults and salt on karst detection. Full elastic simulation was performed on the various ...

Deep earthquakes in subducting slabs hosted in highly anisotropic rock fabric

Analysis of deep subduction-zone earthquakes, those at depths greater than 60 km, reveals the physical and chemical properties of a descending oceanic lithosphere at mantle depths. Over the past five decades, it has been observed that a large fraction of deep earthquakes has non-double-couple (non-DC) seismic radiation patterns. In contrast, shallow earthquakes tend to have DC radiation patterns due to mechanisms of shear faulting. These observations have been used to argue that deep earthquakes rupture differently from shallow earthquakes. Here we show that the observed global distribution of non-DC deep earthquakes could be caused by shear faulting mechanisms, but in a highly anisotropic laminated rock fabric that surrounds the deep earthquakes within subducted slabs. For intermediate-depth earthquakes (~60–300 km), we found a large shear-wave anisotropy of ~25%, possibly caused by laminated fabric or aligned melt pockets oriented parallel to the slab interface, which provides new supporting evidence for the metamorphic dehydration reactions in slabs. However, at deep-focus depths (>300 km), the putative metastable phase-change mechanism alone cannot explain the seismic anisotropy. Instead, our results and those from recent experiments suggest materials such as magnesite, or perhaps carbonatite melt, may play a role in generating deep-focus earthquakes.Radiation patterns for deep earthquakes could be a result of shear faulting mechanisms—similar to those for shallow earthquakes—but in highly anisotropic rock fabric, suggest seismic analyses.

Does Dipole Dispersion Crossover Indicate Borehole Stress-induced Anisotropy?

Crossover of flexural wave dispersion recorded in cross-dipole measurements is interpreted as an indicator of stress-induced anisotropy around a borehole. We investigate different factors that influence flexural wave dispersion. Through numerical modeling, we show that for a circular borehole surrounded by an isotropic formation that is subjected to an anisotropic stress field the dipole flexural dispersion crossover is detectable only when the formation is very compliant. This might happen only in the shallow subsurface or in zones having high pore pressure. However, we show that dipole dispersion crossover can also result from the combined effect of formation intrinsic anisotropy and borehole ellipticity. We find that a small change in borehole ellipticity (e.g. ratio of maximum to minimum borehole radii ~ 1.1) and 1% intrinsic anisotropy can result in a resolvable crossover in flexural dispersion that might be erroneously interpreted as borehole stress-induced anisotropy. A thorough and correct interpretation of flexural dispersion crossover thus has to take into account the effects of both stress-induced and intrinsic anisotropy, and borehole ellipticity.

Modeling of acoustic wave scattering from a two-dimensional fracture

Eni-MIT Energy Initiative Founding Member Program (Eni Multiscale Reservoir Science Project)

Efficient Double-Beam Characterization for Fractured Reservoir

DEDICATED - Case Studies in Diffraction Imaging and Interpretation. We propose an efficient target-oriented method to characterize seismic properties of fractured reservoirs: the spacing between fractures and the fracture orientation. Based on the diffraction theory, the scattered wave vector is related to the incident wave vector computed from the source to the target using a background velocity model. Two Gaussian beams, a source beam constructed along the incident direction and a receiver beam along the scattered direction, interfere with each other. We then scan all possible fracture spacings and orientations and output an interference pattern as a function of the spacing and orientation from which the most likely fracture spacing and orientation can be inferred. Our method is adaptive for a variety of seismic acquisition geometries. If seismic sources (or receivers) are spatially sparse, we can shrink the source (or receiver) beam-width to zero and in this case, we achieve point-source-to-beam interference. We validate our algorithm using a synthetic dataset created by a finite difference scheme with the linear-slip boundary condition, which describes the wave-fracture interaction.