A novel algorithm for evaluating cement azimuthal density based on perturbation theory in horizontal well

Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density.In this regard,this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system.The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory,and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions.Combined with the relationship between gamma-ray counts and cement density,a multi-parameter calculation equation system is established,and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density.This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm^(3) for the cement azimuthal density.This accuracy level is ten times higher compared to density accuracy calculated using calibration equations.Overall,this algorithm enhances the accuracy of cement azimuthal density evaluation,provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.

Effect of variations in the polar and azimuthal angles of coarse particles on the structure of drainage channels in thickened beds

The 3D reconstruction and quantitative characterization of drainage channels and coarse tailings particles in a bed were conducted in this study.The influence of variations in the azimuthal angle(θ)and polar angle(φ)of coarse particles on drainage channel structure was analyzed,and the drainage mechanism of the bed was studied.Results showed that water discharge in the bed reduced the size of pores and throat channels,increasing slurry concentration.The throat channel structure was a key component of the drainage process.Theφandθof particles changed predominantly along the length direction.The changes inφhad a cumulative plugging effect on the drainage channel and increased the difficulty of water discharge.The rake and rod formed a shear ring in the tailings bed with shear,and theθdistribution of particles changed from disorderly to orderly during the rotation process.The drainage channel was squeezed during the shearing process with the change inθ,which broke the channel structure,encouraged water discharge in the bed,and facilitated a further increase in slurry concentration.The findings of this work are expected to offer theoretical guidance for preparing high-concentration underflow in the tailings thickening process.

An Investigation of Purely Azimuthal Passive Localization and Position Adjustment in Attempted UAV Formation Flights

When a cluster of unmanned aerial vehicles (UAVs) is flying in formation, it is crucial to maintain the formation and not to be interfered by external electromagnetic wave signals. In order to maintain the formation, this paper proposes to use pure azimuth passive positioning to adjust the position of UAVs, i.e., certain UAVs in the formation transmit signals, the rest of the UAVs receive the signals passively, and extract the orientation information from them to adjust the position of the UAVs [1] [2] [3]. In this paper, the position adjustment problem of UAVs in “circular” formation flight under three models is investigated. To address the problem of “how to obtain the position of the receiving UAV when there are two UAVs with known numbers and evenly distributed on the circumference in addition to the UAV transmitting at the known center of the circle, and the rest of the UAVs with slight deviations in their positions are receiving the signals”, two purely mathematical geometric methods, namely, triangular localization method and polar co-ordinate method, are proposed respectively. We have determined the position of the receiving UAV;we have used the exhaustive method and the construction and disproof method to solve the problem of “how many UAVs are needed to transmit signals in order to realize the effective positioning of the UAVs when it is known that a certain UAV with a slight deviation in its position receives the signals emitted by two UAVs at the same time”, and the results show that: in addition to the known signals emitted by two UAVs, it is also necessary to transmit the signals emitted by two UAVs. The results show that in addition to the known two UAVs transmitting signals, two additional UAVs are required to transmit signals for precise po-sitioning. When the position of UAVs has deviation at the initial moment, the ideal approximation method and the target delimitation method are pro-posed, and the target of nine UAVs uniformly distributed on a circle of a spe-cific radius is achieved through several adjustments, after which the ad-vantages and disadvantages of each model are analyzed, and suggestions for improvement are put forward. The purely azimuthal passive localization method and the constructed model approach proposed in this paper can be extended to other fields, such as spacecraft formations in space and battle-ship formations at sea, as well as other formation flight position adjustment problems.

Modeling and analysis of azimuthal AVO responses from a viscoelastic anisotropic reflector

We propose a method for mOdeling azimuthal AVO responses from a fractured i reflector. The method calculates the integrated reflected wavetrains, and the wavetrains contain elastodynamic information including the contrast in impedance and anelasticity i across interfaces, the intemal anisotropic propagation, the dispersion and attenuation along i the wave path, and tuning and interference. The results suggest that for large angles of incidence, the velocity dispersion and attenuation increase the amplitudes of PP waves from the top and decrease those from the bottom. For azimuthal responses at specific angles of incidence, the reflected wavetrains of PP waves tend to have longer duration with increasing azimuth. In contrast, model-converted PSV and PSH reflections show stable azimuthal features and are less affected by the reflector thickness. The amplitudes of PSV reflections increase with increasing azimuth; moreover, the waves have no reflection energy at 0° and 90° azimuth and maximum amplitude at 45° azimuth.

Component azimuths of the CEArray stations estimated from P-wave particle motion

The recently built China Digital Seismic Network consists of the China National Digital Seismic Network （CNDSN）, 31 regional seismic networks and several small aperture arrays with more than 1 000 stations including 850＋ broadband stations. It forms a gigantic seismic array that provides an unprecedented opportunity to study the Earth＇s deep interior besides its routine task of seismic monitoring. Many modern seismic studies rely on rotation of vertical and horizontal components in order to separate different types of seismic waves. Knowledge of the orientations of the two horizontal components thus is important to perform a correction rotation. We analyzed particle motions of teleseismic P waves recorded by the network and used them to estimate the northcomponent azimuth of each station. An SNR-weighted-multi-event method was introduced to obtain component azimuths that best explain the P-wave particle motions of all the events recorded at a station. The method provides robust estimates including a measurement error calculated from background noise levels. We found that about one third of the stations have some sort of problems, including misorientation of the two horizontal components, mislabeling and polarity reversal in one or more components. These problems need to be taken into account for any rotation based seismic studies.

Azimuthal elastic impedance-based Fourier coefficient variation with angle inversion for fracture weakness

Quantitative inversion of fracture weakness plays an important role in fracture prediction.Considering reservoirs with a set of vertical fractures as horizontal transversely isotropic media,the logarithmic normalized azimuthal elastic impedance(EI)is rewritten in terms of Fourier coefficients(FCs),the 90°ambiguity in the azimuth estimation of the symmetry axis is resolved by judging the sign of the second FC,and we choose the FCs with the highest sensitivity to fracture weakness and present a feasible inversion workflow for fracture weakness,which involves:(1)the inversion for azimuthal EI datasets from observed azimuthal angle gathers;(2)the prediction for the second FCs and azimuth of the symmetry axis from the estimated azimuthal EI datasets;and(3)the estimation of fracture weakness combining the extracted second FCs and azimuth of the symmetry axis iteratively,which is constrained utilizing the Cauchy sparse regularization and the low-frequency regularization in a Bayesian framework.Tests on synthetic and field data demonstrate that the 90°ambiguity in the azimuth estimation of the symmetry axis has been removed,and reliable fracture weakness can be obtained when the estimated azimuth of the symmetry axis deviates less than 30°,which can guide the prediction of fractured reservoirs.

Study on rate azimuth platform inertial navigation system

The cost of the gravity passive inertial navigation system will be lower witha rate azimuth platform and gravity sensor constituting a gravity measurement and navigationsystem. According to the system performance characteristics, we study the rate azimuth platforminertial navigation system (RAPINS), give the system navigation algorithm, error equations of theattitude, velocity and position of the rate azimuth platform, and random error models of theaccelerometer and gyro. Using the MATLAB/Simulink tools, we study the RAPINS and RAPINS withvelocity damping. Simulation results demonstrate that the RAPINS with velocity damping has smallerrors in platform attitude and position and satisfies gravity measurement and navigationrequirement.

Azimuthal cement evaluation with an acoustic phased-arc array transmitter:numerical simulations and field tests

We developed a novel cement evaluation logging tool,named the azimuthally acoustic bond tool（AABT）,which uses a phased-arc array transmitter with azimuthal detection capability.We combined numerical simulations and field tests to verify the AABT tool.The numerical simulation results showed that the radiation direction of the subarray corresponding to the maximum amplitude of the first arrival matches the azimuth of the channeling when it is behind the casing.With larger channeling size in the circumferential direction,the amplitude difference of the casing wave at different azimuths becomes more evident.The test results showed that the AABT can accurately locate the casing collars and evaluate the cement bond quality with azimuthal resolution at the casing-cement interface,and can visualize the size,depth,and azimuth of channeling.In the case of good casingcement bonding,the AABT can further evaluate the cement bond quality at the cementformation interface with azimuthal resolution by using the amplitude map and the velocity of the formation wave.

Numerical modeling of PP- and PS-wave azimuthal anisotropy in HTI media

This study focuses on the factors that may affect the feasibility of performing elliptical anisotropy analysis on azimuthal PP and PS-wave data in HTI media, with the aim of using the modeling results as guidance in real seismic data application. Our results reveal that there is an offset limitation for both PP- and PS-waves in elliptical anisotropy fitting, and that PS-waves show a wider applicable offset range and larger observable azimuthal anisotropy than PP-waves. The major axis of the elliptical fit to the amplitudes of the R-component is perpendicular to the fracture strike, which is opposite to that in PP-wave analysis. The azimuthal interval travel time of PS-waves shows a nearly elliptical distribution and the major axis of the fit ellipse is perpendicular to the fracture strike, which is same as that in PP-wave analysis. For data within the applicable offset range, the anisotropic magnitude obtained from amplitude and travel time attributes of PP- and PS-waves exhibits a dependence on fracture density, and the major to minor axis ratio of the fit ellipse may be used to infer the relative distribution of fracture densities.

On the Azimuth Error of ESG Strapdown North-Seeking Instrument

Because the vector of angular momentum of ESG (electrostatically suspended gyroscope) maintains the fixed direction in inertial space, it may be regarded as a fixed star. The astronavigation aigorithm is used to estimate the azimuth angle and the gyro constant drift in the paper. The relative errors which affect the estimation accuracy of the azimuth angle are the analysed.

Crustal anisotropy of Taihang Mountain Range using azimuthal variation of receiver functions

摘要探讨了利用接收函数方位变化研究各向异性复杂地区速度结构的可能性。详细介绍了具有任意对称轴方向的横向各向同性系统中介质响应的计算过程，并将利用接收函数方位变化研究地壳各向异性的方法应用于华北太行山地区。结果表明，研究台站下方地壳具有明显的各向异性特征，其中地表盖层表现为8％-15％的慢轴型各向异性；深部地壳各向异性略小，表现为3％-5％的快轴型各向异性特征,不同台站获得的各向异性对称轴的方向及深度分布不具有明显的一致性,区域构造环境的变化可能是导致地壳各向异性存在的原斟。

Fracture detection by using full azimuth P wave attributes

A type of specific fractured hydrocarbon reservoir, a shale fractured reservoir, exists in the Shengli oilfield. Due to very small porosity of this type, low sensitivity to the variation of petrochemical property parameters, and strong anisotropy, it is very difficult to explore for them. So far, there is no set of mature methods for recognition of direction, distribution, and density of the fractures by an integrated analysis of geologic, geophysical, well log, drilling data, and etc. This paper presents a new method for acoustic impedance variation with azimuth （IPVA）, based on existing fracture detection methods. Seismic acquisition, processing, and recognition techniques were developed for detecting directional vertical fractures using multi-azimuth P wave data in combination with the seismic and geological features of shale fractures in the Luojia area. The IPVA research is carried out for recognizing the distribution, strike, and density of fractures based on the study of velocity variation with azimuth （VVA） and amplitude variation with azimuth （AVA） for full azimuth P wave data at different CMP positions. Through practical application in the Luojia area, primary results have been obtained which verifies that the IPVA method provides good potential for quantitative detection of parallel, high angle, shale fractures.

P-wave fracture prediction algorithm using pre-stack data with limited azimuth distribution:A case study in the TZ45 area,Tarim Basin,China

Fractured reservoirs always show anisotropic amplitude features,i.e.the reflection amplitude of seismic waves varies with offset and azimuth （AVOZ）.A noise attenuation fracture inversion algorithm is presented for fracture detection based on P-wave AVOZ.The conventional inversion method always fails when applied to limited azimuth data because of the existence of noise.In our inversion algorithm,special attention is paid to suppressing the noise during inversion,to overcome the limitation of the conventional inversion method on limited azimuth data.Numerical models are employed to illustrate the effectiveness of the method.The inversion algorithm is then applied to Tazhong 45 area field data which is acquired under limited azimuth distribution.Compared with cores and fullbore formation microimage （FMI）,the inverted results （fracture density and orientation） are reasonable,suggesting that the inversion algorithm is feasible for fracture prediction in the Tarim Basin.

ulti-azimuth three-component surface seismic modeling for viscoelastic cracked monoclinic media

In this article, a method of high order, staggered grid, finite difference was used to model snapshots of seismic wave propagation and multi-azimuth surface seismic records in viscoelastic cracked monoclinic media. The modeling results clearly show the anisotropy caused by the crack fill material and the viscoelastic wave field through the monoclinic media. Summarizing the regularity of seismic records for different azimuths, this study is a significant attempt to understand the wave fields propagated in real media and to propose a more rational theoretical model for the future.

A method for inversion of layered shear wavespeed azimuthal anisotropy from Rayleigh wave dispersion using the Neighborhood Algorithm

Seismic anisotropy provides important constraints on deformation patterns of Earth＇s material. Rayleigh wave dispersion data with azimuthal anisotropy can be used to invert for depth-dependent shear wavespeed azimuthal anisotropy, therefore reflecting depth-varying deformation patterns in the crust and upper mantle. In this study, we propose a two-step method that uses the Neighborhood Algorithm （NA） for the point-wise inversion of depth-dependent shear wavespeeds and azimuthal anisotropy from Rayleigh wave azimuthally anisotropic dispersion data. The first step employs the NA to estimate depth- dependent Vsv （or the elastic parameter L） as well as their uncertainties from the isotropic part Rayleigh wave dispersion data. In the second step, we first adopt a difference scheme to compute approximate Rayleigh-wave phase velocity sensitivity kernels to azimuthally anisotropic parameters with respect to the velocity model obtained in the first step. Then we perform the NA to estimate the azimuthally anisotropic parameters Gc/L and Gs/L at depths separately from the corresponding cosine and sine terms of the azimuthally anisotropic dispersion data. Finally, we compute the depth-dependent magnitude and fast polariza- tion azimuth of shear wavespeed azimuthal anisotropy. The use of the global search NA and Bayesian analysis allows for more reliable estimates of depth-dependent shear wavespeeds and azimuthal anisotropy as well as their uncertainties.We illustrate the inversion method using the azimuthally anisotropic dispersion data in SE Tibet, where we find apparent changes of fast axes of shear wavespeed azimuthal anisotropy between the crust and uppermost mantle.

Detection performance and inversion processing of logging-while-drilling extra-deep azimuthal resistivity measurements

We present systematic investigations on the physics,detection performance and inversion of logging-while-drilling extradeep azimuthal resistivity measurements(EDARM).First,the definitions of EDRAM measurements are discussed,followed by the derivation of the attenuation and phase-shift geometrical factors to illustrate the relative contributions of formation units to the observed signals.Then,a new definition of detection depth,which considers the uncertainty of inversion results caused by the data noise,is proposed to quantify the detection capability of ED ARM.Finally,the B ayesian theory associated with Markov chain Monte Carlo sampling is introduced for fast processing of EDARM data.Numerical results show that ED ARM is capable of detecting the azimuth and distance of remote bed boundaries,and the detection capability increases with increasing spacing and resistivity contrast.The EDARM tool can accommodate a large range of formation resistivity and is able to provide the resistivity anisotropy at arbitrary relative dipping angles.In addition,multiple bed boundaries and reservoir images near the borehole are readily obtained by using the Bayesian inversion.

Wide/narrow azimuth acquisition footprints and their effects on seismic imaging

Acquisition footprint is a new concept to describe the seismic noise in three-dimensional seismic exploration and it is closely related to geometry and observation shuttering. At present, the study on acquisition footprints has become a hot spot. In partnership with the Dagang Oilfield, we used the channel sand body seismic physical model to study the characteristics of wide/narrow azimuth acquisition footprints and analyzed and compared the two types of footprints and their effects on target imaging. In addition, the footprints caused by data processing of the normal moveout offset （NMO） stretching aberration were discussed. These footprints are located only in the shallow or middle layer in the time slice, and possibly affect the imaging of shallow target layers, and have no influence on deep target imaging. Seismic physical modeling has its advantages in the study of acquisition footprints.

Efficient finite-volume simulation of the LWD orthogonal azimuth electromagnetic response in a three-dimensional anisotropic formation using potentials on cylindrical meshes

In this study,the cylindrical finite-volume method(FVM)is advanced for the efficient and high-precision simulation of the logging while drilling(LWD)orthogonal azimuth electromagnetic tool(OAEMT)response in a three-dimensional(3 D)anisotropic formation.To overcome the ill-condition and convergence problems arising from the low induction number,Maxwell’s equations are reformulated into a mixed Helmholtz equation for the coupled potentials in a cylindrical coordinate system.The electrical fi eld continuation method is applied to approximate the perfectly electrical conducting(PEC)boundary condition,to improve the discretization accuracy of the Helmholtz equation on the surface of metal mandrels.On the base,the 3 D FVM on Lebedev’s staggered grids in the cylindrical coordinates is employed to discretize the mixed equations to ensure good conformity with typical well-logging tool geometries.The equivalent conductivity in a non-uniform element is determined by a standardization technique.The direct solver,PARDISO,is applied to efficiently solve the sparse linear equation systems for the multi-transmitter problem.To reduce the number of calls to PARDISO,the whole computational domain is divided into small windows that contain multiple measuring points.The electromagnetic(EM)solutions produced by all the transmitters per window are simultaneously solved because the discrete matrix,relevant to all the transmitters in the same window,is changed.Finally,the 3 D FVM is validated against the numerical mode matching method(NMM),and the characteristics of both the coaxial and coplanar responses of the EM field tool are investigated using the numerical results.

Forecasting Fractures in Coal Seams by Using Azimuthal Anisotropy from P-Wave Seismic Data

If the thickness of coal seams and the lithology of both roofs and floors of coal seams have not changed at all or only a little, then it is thought that the elastic anisotropy of coal seams depends mainly on fractures and obeys the horizontally symmetric model of an azimuth anisotropy. For a fixed offset, the amplitude A of the reflection P-wave and the cosine of 2φ has an approximately linear relation, (φ is the source-detector azimuth with respect to the fracture strike. Based on this relationship, many things can be done, such as the extraction of macro bins, the correction of residual normal moveout, the formation of azimuth gather, the transformation and normalization of azimuth gathers and the extraction of reflection wave amplitudes of coal seams. The least squares method was used to inverse theoretically the direction and density of fractures of coal seams. The result is in good agreement with the regional geological structure, indicating that the azimuth anisotropic analysis of the P-wave is feasible in evaluating the density and direction of fractures in coal seams.

Detection performance of azimuthal electromagnetic logging while drilling tool in anisotropic media

Azimuthal electromagnetic(EM)logging while drilling(LWD)has been extensively used in high-angle and horizontal(HA/HZ)wells.However,due to the effects of formation anisotropy,accurate geosteering decision and formation evaluations have become increasingly difficult.To quantitatively analyze the effect of anisotropy on tool responses and data processing,this paper investigates the sensitivity of EM LWD measurements to electric anisotropy and inversion accuracy via forward modeling and inversion.First,a sensitivity factor is defined to quantitatively analyze the sensitivity of the magnetic field components and synthetic signals to electric anisotropy.Then,azimuthal EM LWD responses in anisotropic layered formations are simulated,and the sensitivities to formation parameters for compensated and uncompensated tool configurations are comparatively analyzed.Finally,we discuss the effects of the inversion model on bed boundary inversion in anisotropic formations.Numerical simulation and inversion results show that azimuthal EM LWD can be significantly affected by electric anisotropy.Fortunately,by using a symmetrical compensation configuration,the sensitivity of the geosignals to electric anisotropy can be suppressed,and the boundary detection capability can be further enhanced.Anisotropy normally gives rise to separated resistivity curves and abnormal"horns";moreover,complicated nonlinear distortion can also arise in geosignals as the tool approaches a bed boundary.If anisotropy effects are ignored in the inversion process,the estimated bed boundary and formation resistivity are usually unreliable,which may mislead geosteering decisions.