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.

Zoeppritz-based AVO inversion using an improved Markov chain Monte Carlo method

The conventional Markov chain Monte Carlo （MCMC） method is limited to the selected shape and size of proposal distribution and is not easy to start when the initial proposal distribution is far away from the target distribution. To overcome these drawbacks of the conventional MCMC method, two useful improvements in MCMC method, adaptive Metropolis （AM） algorithm and delayed rejection （DR） algorithm, are attempted to be combined. The AM algorithm aims at adapting the proposal distribution by using the generated estimators, and the DR algorithm aims at enhancing the efficiency of the improved MCMC method. Based on the improved MCMC method, a Bayesian amplitude versus offset （AVO） inversion method on the basis of the exact Zoeppritz equation has been developed, with which the P- and S-wave velocities and the density can be obtained directly, and the uncertainty of AVO inversion results has been estimated as well. The study based on the logging data and the seismic data demonstrates the feasibility and robustness of the method and shows that all three parameters are well retrieved. So the exact Zoeppritz-based nonlinear inversion method by using the improved MCMC is not only suitable for reservoirs with strong-contrast interfaces and longoffset ranges but also it is more stable, accurate and antinoise.

Estimation of fracture density and orientation from azimuthal elastic impedance difference through singular value decomposition

Accurate estimation of fracture density and orientation is of great significance for seismic characterization of fractured reservoirs.Here,we propose a novel methodology to estimate fracture density and orientation from azimuthal elastic impedance(AEI)difference using singular value decomposition(SVD).Based on Hudson's model,we first derive the AEI equation containing fracture density in HTI media,and then obtain basis functions and singular values from the normalized AEI difference utilizing SVD.Analysis shows that the basis function changing with azimuth is related to fracture orientation,fracture density is the linearly weighted sum of singular values,and the first singular value contributes the most to fracture density.Thus,we develop an SVD-based fracture density and orientation inversion approach constrained by smooth prior elastic parameters.Synthetic example shows that fracture density and orientation can be stably estimated,and the correlation coefficient between the true value and the estimated fracture density is above 0.85 even when an S/N ratio of 2.Field data example shows that the estimated fracture orientation is consistent with the interpretation of image log data,and the estimated fracture density reliably indicates fractured gas-bearing reservoir,which could help to guide the exploration and development of fractured reservoirs.

The construction of shale rock physics model and brittleness prediction for high-porosity shale gas-bearing reservoir

Due to the huge differences between the unconventional shale and conventional sand reservoirs in many aspects such as the types and the characteristics of minerals,matrix pores and fluids,the construction of shale rock physics model is significant for the exploration and development of shale reservoirs.To make a better characterization of shale gas-bearing reservoirs,we first propose a new but more suitable rock physics model to characterize the reservoirs.We then use a well A to demonstrate the feasibility and reliability of the proposed rock physics model of shale gas-bearing reservoirs.Moreover,we propose a new brittleness indicator for the high-porosity and organic-rich shale gas-bearing reservoirs.Based on the parameter analysis using the constructed rock physics model,we finally compare the new brittleness indicator with the commonly used Young’s modulus in the content of quartz and organic matter,the matrix porosity,and the types of filled fluids.We also propose a new shale brittleness index by integrating the proposed new brittleness indicator and the Poisson’s ratio.Tests on real data sets demonstrate that the new brittleness indicator and index are more sensitive than the commonly used Young’s modulus and brittleness index for the high-porosity and high-brittleness shale gas-bearing reservoirs.

Fluid discrimination incorporating viscoelasticity and frequency-dependent amplitude variation with offsets inversion

Frequency-dependent amplitude versus offset(FAVO)inversion is a popular method to estimate the frequency-dependent elastic parameters by using amplitude and frequency information of pre-stack seismic data to guide fluid identification.Current frequency-dependent AVO inversion methods are mainly based on elastic theory without the consideration of the viscoelasticity of oil/gas.A fluid discrimination approach is proposed in this study by incorporating the viscoelasticity and relevant FAVO inversion.Based on viscoelastic and rock physics theories,a frequency-dependent viscoelastic solid-liquid decoupling fluid factor is initially constructed,and its sensitivity in fluid discrimination is compared with other conventional fluid factors.Furthermore,a novel reflectivity equation is derived in terms of the viscoelastic solid-liquid decoupling fluid factor.Due to the introduction of viscoelastic theory,the proposed reflectivity is related to frequency,which is more widely applicable than the traditional elastic reflectivity equation directly derived from the elastic reflectivity equation on frequency.Finally,a pragmatic frequency-dependent inversion method is introduced to verify the feasibility of the equation for frequency-dependent viscoelastic solid-liquid decoupling fluid factor prediction.Synthetic and field data examples demonstrate the feasibility and stability of the proposed approach in fluid discrimination.

Seismic fluid identification using a nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo method

Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.

Elastic impedance inversion for stress indicator in weakly orthorhombic media

Hydraulic fracturing is a crucial technology for improving permeability and production of shale reservoirs.The precise estimation of the stress distribution has a significant guidance for optimizing the placement of hydraulic fracturing.Assuming that the shale gas reservoir is a weakly anisotropic medium with orthorhombic symmetry,a new stress indicator parameterized by rock mechanical parameters and fracture parameters is firstly presented to predict the differential horizontal stress ratio in shale gas reservoirs.Then,we derive a novel simplified P-to-P reflection coefficient and a logarithmic normalized elastic impedance(EI)as a function of Young’s modulus,Poisson’s ratio,Thomsen’s WA parameterδband normal excess compliance Z_(N).Next,we adopt azimuthal EI inversion in a Bayesian framework to estimate rock mechanics parameters and fracture parameters directly on a fractured shale gas field seismic data.Finally,the stress indicator is determined by utilizing four inverted parameters.Synthetic examples demonstrate that the proposed approach produces stable parameter estimates even with moderate noise,verifying the feasibility and effectiveness of the method.Test on a field data set illustrates that the inversion results can be reasonably estimated,and the stress indicator derived by the inversion accords with the geomechanics result.Compared with the previous method,the new stress indicator has a higher capability to describe stress characteristics in the shale reservoir.We conclude that this stress evaluation procedure can provide reliable guidance for well location deployment and hydraulic fracturing reformation.