Single-step probabilistic inversion of 3D seismic data of a carbonate reservoir in Southwest Iran

We use a sampling-based Markov chain Monte Carlo method to invert seismic data directly for porosity and quantify its uncertainty distribution in a hard-rock carbonate reservoir in Southwest Iran. The noise that remains on seismic data after the processing flow is correlated with the bandwidth in the range of the seismic wavelet. Hence, to account for the inherent correlated nature of the band-limited seismic noise in the probabilistic inversion of real seismic data, we assume the estimated seismic wavelet as a suitable proxy for capturing the coupling of noise samples. In contrast to the common approach of inserting a delta function on the main diagonal of the covariance matrix, we insert the seismic wavelet on its main diagonal. We also calibrate an empirical and a semi-empirical inclusion-based rock-physics model to characterize the rock-frame elastic moduli via a lithology constrained fitting of the parameters of these models, i.e. the critical porosity and the pore aspect ratio. These calibrated rock-physics models are embedded in the inversion procedure to link petrophysical and elastic properties. In addition, we obtain the pointwise critical porosity and pore aspect ratio, which can potentially facilitate the interpretation of the reservoir for further studies. The inversion results are evaluated by comparing with porosity logs and an existing geological model (porosity model) constructed through a geostatistical simulation approach. We assess the consistency of the geological model through a geomodel-to-seismic modeling approach. The results confirm the performance of the probabilistic inversion in resolving some thin layers and reconstructing the observed seismic data. We present the applicability of the proposed sampling-based approach to invert 3D seismic data for estimating the porosity distribution and its associated uncertainty for four subzones of the reservoir. The porosity time maps and the facies probabilities obtained via porosity cut-offs indicate the relative quality of the reservoir’s subzones.

Porosity dependence of elastic moduli of snow and firn

Measurements of elastic wave velocities enable non-destructive estimation of the mechanical properties, elastic moduli and density of snow and firn. The variation of elastic moduli with porosity in dry snow and firn is modeled using a differential effective medium scheme modified to account for the critical porosity above which the bulk and shear moduli of the ice frame vanish. A comparison of predicted and measured elastic moduli indicates that the shear modulus of ice in snow is lower than that computed from single crystal elastic stiffnesses of ice. This may indicate that the bonds between snow particles are more deformable under shear than under compression. A partial alignment of ice crystals also may contribute. Good agreement between elastic stiffnesses of the ice frame obtained from elastic wave velocity measurements and the predictions of the theory is observed. The approach is simple and compact, and does not require the use of empirical fits to the data. Owing to its simplicity, this model may prove useful in a variety of potential applications such as construction on snow, interpretation of seismic measurements to monitor and locate avalanches and estimation of density within compacting snow deposited on glaciers and ice sheets.

Finite element simulation of ductile fracture in polycrystalline materials using a regularized porous crystal plasticity model

In the present study, a hypoelastic–plastic formulation of porous crystal plasticity with a regularized version of Schmid’s law is proposed. The equation describing the effect of the voids on plasticity is modified to allow for an explicit analytical solution for the effective resolved shear stress. The regularized porous crystal plasticity model is implemented as a material model in a finite element code using the cutting plane algorithm. Fracture is described by element erosion at a critical porosity. The proposed model is used for two test cases of two- and three-dimensional polycrystals deformed in tension until full fracture is achieved. The simulations demonstrate the capability of the proposed model to account for the interaction between different modes of strain localization, such as shear bands and necking, and the initiation and propagation of ductile fracture in large scale polycrystal models with detailed grain description and realistic boundary conditions.

Velocity-Porosity-Mineralogy Model for Unconventional Shale and Its Applications to Digital Rock Physics

By examining wireline data from Woodford and Wolfcamp gas shale, we find that the primary controls on the elastic-wave velocity are the total porosity, kerogen content, and mineralogy. At a fixed porosity, both Vp and Vs strongly depend on the clay content, as well as on the kerogen content. Both velocities are also strong functions of the sum of the above two components. Even better discrimination of the elastic properties at a fixed porosity is attained if we use the elastic-wave velocity of the solid matrix (including kerogen) of rock as the third variable. This finding, fairly obvious in retrospect, helps combine all mineralogical factors into only two variables, Vp and Vs of the solid phase. The constant-cement rock physics model, whose mathematical form is the modified lower Hashin-Shtrikman elastic bound, accurately describes the data. The inputs to this model include the elastic moduli and density of the solid component (minerals plus kerogen), those of the formation fluid, the differential pressure, and the critical porosity and coordination number (the average number of grain-to-grain contacts at the critical porosity). We show how this rock physics model can be used to predict the elastic properties from digital images of core, as well as 2D scanning electron microscope images of very small rock fragments.

Seismic AVO statistical inversion incorporating poroelasticity

Seismic amplitude variation with offset (AVO) inversion is an important approach for quantitative prediction of rock elasticity, lithology and fluid properties. With Biot–Gassmann’s poroelasticity, an improved statistical AVO inversion approach is proposed. To distinguish the influence of rock porosity and pore fluid modulus on AVO reflection coefficients, the AVO equation of reflection coefficients parameterized by porosity, rock-matrix moduli, density and fluid modulus is initially derived from Gassmann equation and critical porosity model. From the analysis of the influences of model parameters on the proposed AVO equation, rock porosity has the greatest influences, followed by rock-matrix moduli and density, and fluid modulus has the least influences among these model parameters. Furthermore, a statistical AVO stepwise inversion method is implemented to the simultaneous estimation of rock porosity, rock-matrix modulus, density and fluid modulus. Besides, the Laplace probability model and differential evolution, Markov chain Monte Carlo algorithm is utilized for the stochastic simulation within Bayesian framework. Models and field data examples demonstrate that the simultaneous optimizations of multiple Markov chains can achieve the efficient simulation of the posterior probability density distribution of model parameters, which is helpful for the uncertainty analysis of the inversion and sets a theoretical fundament for reservoir characterization and fluid discrimination.

A Workflow Incorporating an Artificial Neural Network to Predict Subsurface Porosity for CO2 Storage Geological Site Characterization

The large scale and complexity of Carbon, Capture, Storage (CCS) projects necessitates time and cost saving strategies to strengthen investment and widespread deployment of this technology. Here, we successfully demonstrate a novel geologic site characterization workflow using an Artificial Neural Network (ANN) at the Southeast Regional Carbon Anthropogenic Test in Citronelle, Alabama. The Anthropogenic Test Site occurs within the Citronelle oilfield which contains hundreds of wells with electrical logs that lack critical porosity measurements. Three new test wells were drilled at the injection site and each well was paired with a nearby legacy well containing vintage electrical logs. The test wells were logged for measurements of density porosity and cored over the storage reservoir. An Artificial Neural Network was developed, trained, and validated using patterns recognized between the between vintage electrical logs and modern density porosity measurements at each well pair. The trained neural network was applied to 36 oil wells across the Citronelle Field and used to generate synthetic porosities of the storage reservoir and overlying stratigraphy. Ultimately, permeability of the storage reservoir was estimated using a combination of synthetic porosity and an empirically derived relationship between porosity and permeability determined from core.

Influence of Strain Rate Sensitivity on Localization and Void Coalescence

The onset of macroscopic strain localization limits the ductility of many ductile materials. For porous ductile materials, two distinct mechanisms of macroscopic localization have been identified: void growth induced softening and void coalescence. In this work we focus on analyzing the influence of material's strain rate sensitivity (SRS) on the two mechanisms of macroscopic localization or ductile failure as a function of the imposed stress triaxiality. To this end, three dimensional finite element calculations of unit cells have been carried out to model void growth and coalescence in an infinite block containing a periodic distribution of initially spherical voids in a band. The matrix material of the unit cell is considered to follow a strain rate dependent elastic perfectly plastic flow response. The unit cell calculations are carried out for a range of SRS parameter, imposed stress triaxiality and initial orientations of the voided band. Our results show that both the critical porosity and strain at the onset of localization and coalescence are strongly influenced by the SRS parameter and the imposed stress triaxiality values. Furthermore, the relative effect of the SRS parameter is found to increases with the increasing value of the imposed stress triaxiality.

Influence of Strain rate sensitivity on Localization and void coalescence

The onset of macroscopic strain localization limits the ductility of many ductile materials. For porous ductile materials, two distinct mechanisms of macroscopic localization have been identified: void growth induced softening and void coalescence. In this work we focus on analyzing the influence of materials strain rate sensitivity (SRS) on the two mechanisms of macroscopiclocalization or ductile failure as a function of the imposed stress triaxiality. To this end, threedimensional finite element calculations of unit cells have been carried out to model void growthand coalescence in an infinite block containing a periodic distribution of initially spherical voidsin a band. The matrix material of the unit cell is considered to follow a strain rate dependentelastic perfectly plastic flow response. The unit cell calculations are carried out for a range ofSRS parameter, imposed stress triaxiality and initial orientations of the voided band. Our resultsshow that both the critical porosity and strain at the onset of localization and coalescence are strongly influenced by the SRS parameter and the imposed stress triaxiality values. Furthermore, the relative e?ect of the SRS parameter is found to increases with the increasing value of theimposed stress triaxiality.