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 d[subscript 0]. The optimal parameter space for the maximum value of the linear frequency-shifted factor (α[subscript 0]) and the scaling factor (β[subscript 0]) 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.National Natural Science Foundation (China) (Grant 41174118)Postdoctoral Fellowship of China (Grant 2013M530106)China Scholarship Council (Grant 2010644006)Major State S&T Special Project (Grant 2008ZX05020-004

Simulation of the effect of stress-induced anisotropy on borehole compressional wave propagation

Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This can lead to an incorrect estimation of formation elastic properties measured from sonic logs. Previous work has focused on estimating the elastic properties of the formation surrounding a borehole under anisotropic stress loading. We studied the effect of borehole stress concentration on sonic logging in a moderately consolidated Berea sandstone using a two-step approach. First, we used an iterative approach, which combines a rock-physics model and a finite-element method, to calculate the stress-dependent elastic properties of the rock around a borehole subjected to an anisotropic stress loading. Second, we used the anisotropic elastic model obtained from the first step and a finite-difference method to simulate the acoustic response of the borehole. Although we neglected the effects of rock failure and stress-induced crack opening, our modeling results provided important insights into the characteristics of borehole P-wave propagation when anisotropic in situ stresses are present. Our simulation results were consistent with the published laboratory measurements, which indicate that azimuthal variation of the P-wave velocity around a borehole subjected to uniaxial loading is not a simple cosine function. However, on field scale, the azimuthal variation in P-wave velocity might not be apparent at conventional logging frequencies. We found that the low-velocity region along the wellbore acts as an acoustic focusing zone that substantially enhances the P-wave amplitude, whereas the high-velocity region caused by the stress concentration near the borehole results in a significantly reduced P-wave amplitude. This results in strong azimuthal variation of P-wave amplitude, which may be used to infer the in situ stress state

Granular Packings: Nonlinear elasticity, sound propagation and collective relaxation dynamics

Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of contact elasticity. Moreover, the ratio between the moduli is found to be larger than the prediction of the elastic theory by a constant value. The understanding of these discrepancies has been a longstanding question in the field of granular matter. Here we perform a test of the applicability of elasticity theory to granular materials. We perform sound propagation experiments, numerical simulations and theoretical studies to understand the elastic response of a deforming granular assembly of soft spheres under isotropic loading. Our results for the behavior of the elastic moduli of the system agree very well with experiments. We show that the elasticity partially describes the experimental and numerical results for a system under compressional loads. However, it drastically fails for systems under shear perturbations, particularly for packings without tangential forces and friction. Our work indicates that a correct treatment should include not only the purely elastic response but also collective relaxation mechanisms related to structural disorder and nonaffine motion of grains.Comment: 21 pages, 13 figure

Frequency-dependent attenuation and elasticity in unconsolidated earth materials: effect of damping

We use the Discrete Element Method (DEM) to understand the underlying attenuation mechanism in granular media, with special applicability to the measurements of the so-called effective mass developed earlier. We consider that the particles interact via Hertz-Mindlin elastic contact forces and that the damping is describable as a force proportional to the velocity difference of contacting grains. We determine the behavior of the complex-valued normal mode frequencies using 1) DEM, 2) direct diagonalization of the relevant matrix, and 3) a numerical search for the zeros of the relevant determinant. All three methods are in strong agreement with each other. The real and the imaginary parts of each normal mode frequency characterize the elastic and the dissipative properties, respectively, of the granular medium. We demonstrate that, as the interparticle damping, $\xi$, increases, the normal modes exhibit nearly circular trajectories in the complex frequency plane and that for a given value of $\xi$ they all lie on or near a circle of radius $R$ centered on the point $-iR$ in the complex plane, where $R\propto 1/\xi$. We show that each normal mode becomes critically damped at a value of the damping parameter $\xi \approx 1/\omega_n^0$, where $\omega_n^0$ is the (real-valued) frequency when there is no damping. The strong indication is that these conclusions carry over to the properties of real granular media whose dissipation is dominated by the relative motion of contacting grains. For example, compressional or shear waves in unconsolidated dry sediments can be expected to become overdamped beyond a critical frequency, depending upon the strength of the intergranular damping constant.Comment: 28 pages, 7 figure

Recent advances in theory and technology of oil and gas geophysics

Oil and gas are important energy resources and industry materials. They are stored in pores and fractures of subsurface rocks over thousands of meters in depth, making the finding and distinguishing them to be a significant challenge. The geophysical methods, especially the seismic and well-logging methods, are the effective ways to identify the oil and gas reservoirs and are widely used in industry. Due to the complexity of near surface and subsurface structures of new exploration targets, the geophysical methods based on advanced computation methods and physical principles are continuously proposed to cope with the emerging challenges. Thus, some new advances in theory and technology of oil and gas geophysics are summarized in this editorial material, especially focusing on the geophysical data processing, numerical simulation technology, rock physics modeling, and reservoir characterization.Document Type: EditorialCited as: Wang, Y., Liu, Y., Zou, Z., Bao, Q., Zhang, F., Zong, Z. Recent advances in theory and technology of oil and gas geophysics. Advances in Geo-Energy Research, 2023, 9(1): 1-4. https://doi.org/10.46690/ager.2023.07.0

Effect of borehole stress concentration on compressional wave velocity measurements

Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This could lead to a biased estimation of formation elastic properties measured from sonic logging data. To study the effect of stress concentration around a borehole on sonic logging, we first use an iterative approach, which combines a rock physics model and a finite-element method, to calculate the stress-dependent elastic properties of the rock around a borehole when it is subjected to an anisotropic stress loading. Then we use the anisotropic elastic model obtained from the first step and a finite-difference method to simulate the acoustic response in a borehole. Our numerical results are consistent with published laboratory measurements of the azimuthal velocity variations caused by borehole stress concentration. Both numerical and experimental results show that the variation of P-wave velocity versus azimuth has broad maxima and cusped minima, which is different from the presumed cosine behavior. This is caused by the preference of the wavefield to propagate through a higher velocity region

Analysis Of Pressure Distribution Along Pipeline Blockage Based On The Cfd Simulation

Pipeline blockage, which results from solid and hydrocarbon deposition caused by changes in pressure, temperature, or composition, is a critical issue in oil & gas production and transportation systems. Sometimes blockage, which extends several miles in the long-distance pipeline, can be assumed as a new pipe with a smaller diameter. Therefore, it is imperative to detect the location and size of blockage in pipelines more accurately and efficiently to reduce the number of pipeline accidents. This paper explores the distribution of pressure and pressure gradient through the pipeline without/with single blockage under different operating conditions. 3-dimensional (3D) computational fluid dynamic (CFD) simulations under steady state are carried out to examine the effects of blockage location, blockage diameter and blockage length. The orthogonal array testing technique is applied to study the extent to which factor affects the pressure drop most. The dimensionless parameters like dimensionless blockage location, dimensionless blockage diameter, dimensionless blockage length and dimensionless pressure drop, are introduced to evaluate the relationship among the pressure drop and blockage characterizations. Three fitting formulas of dimensionless parameters distribution are proposed and could be used to locate the pipeline blockage and estimate its diameter and length as well. Finally, laboratory experiments were run to validate the blockage prediction model. The fluid frictional apparatus is modified by replacing part of the pipe with a section of small diameter pipe to simulate the actual partial blockade pipeline. The obtained deviations of pressure drop between the lab experiment result and the prediction model is limited to under 30%. Therefore, the deviation should be taken into account while assessing the blockage through the pipeline based on the blockage prediction model, which also allow the operator to assess partial blockage efficiently and economically