Correlations of Rock-Physics Model Parameters From Bayesian Analysis: Pressure- and Porosity-Dependent Models Applied to Unconsolidated Sands

Correlations of rock-physics model inputs are important to know to help design informative prior models within integrated reservoir-characterization workflows. A Bayesian framework is optimal to determine such correlations. Within that framework, we use velocity and porosity measurements on unconsolidated, dry, and clean sands. Three pressure- and three porosity-dependent rock-physics models are applied to the data to examine relationships among the inputs. As with any Bayesian formulation, we define a prior model and calculate the likelihood in order to evaluate the posterior. With relatively few inputs to consider for each rock-physics model, we found that sampling the posterior exhaustively to be convenient. The results of the Bayesian analyses are multivariate histograms that indicate most likely values of the input parameters given the data to which the rock-physics model was fit. When the Bayesian procedure is repeated many times for the same data, but with different prior models, correlations emerged among the input parameters in a rock-physics model. These correlations were not known previously. Implications, for the pressure- and porosity-dependent models examined here, are that these correlations should be utilized when applying these models to other relevant data sets. Furthermore, additional rock-physics models should be examined similarly to determine any potential correlations in their inputs. These correlations can then be taken advantage of in forward and inverse problems posed in reservoir characterization.

Digital Rock Typing DRT Algorithm Formulation with Optimal Supervised Semantic Segmentation

<p><a></a>Each grid block in a 3D geological model requires a rock type that represents all physical and chemical properties of that block. The properties that classify rock types are lithology, permeability, and capillary pressure. Scientists and engineers determined these properties using conventional laboratory measurements, which embedded destructive methods to the sample or altered some of its properties (i.e., wettability, permeability, and porosity) because the measurements process includes sample crushing, fluid flow, or fluid saturation. Lately, Digital Rock Physics (DRT) has emerged to quantify these properties from micro-Computerized Tomography (uCT) and Magnetic Resonance Imaging (MRI) images. However, the literature did not attempt rock typing in a wholly digital context. We propose performing Digital Rock Typing (DRT) by: (1) integrating the latest DRP advances in a novel process that honors digital rock properties determination, while; (2) digitalizing the latest rock typing approaches in carbonate, and (3) introducing a novel carbonate rock typing process that utilizes computer vision capabilities to provide more insight about the heterogeneous carbonate rock texture.<br></p>

Digital Rock Typing DRT Algorithm Formulation with Optimal Supervised Semantic Segmentation

<p><a></a>Each grid block in a 3D geological model requires a rock type that represents all physical and chemical properties of that block. The properties that classify rock types are lithology, permeability, and capillary pressure. Scientists and engineers determined these properties using conventional laboratory measurements, which embedded destructive methods to the sample or altered some of its properties (i.e., wettability, permeability, and porosity) because the measurements process includes sample crushing, fluid flow, or fluid saturation. Lately, Digital Rock Physics (DRT) has emerged to quantify these properties from micro-Computerized Tomography (uCT) and Magnetic Resonance Imaging (MRI) images. However, the literature did not attempt rock typing in a wholly digital context. We propose performing Digital Rock Typing (DRT) by: (1) integrating the latest DRP advances in a novel process that honors digital rock properties determination, while; (2) digitalizing the latest rock typing approaches in carbonate, and (3) introducing a novel carbonate rock typing process that utilizes computer vision capabilities to provide more insight about the heterogeneous carbonate rock texture.<br></p>

Monitoring geological storage of CO2 using a new rock physics model

To mitigate the global warming crisis, one of the effective ways is to capture CO2 at an emitting source and inject it underground in saline aquifers, depleted oil and gas reservoirs, or in coal beds. This process is known as carbon capture and storage (CCS). With CCS, CO2 is considered a waste product that has to be disposed of properly, like sewage and other pollutants. While and after CO2 injection, monitoring of the CO2 storage site is necessary to observe CO2 plume movement and detect potential leakage. For CO2 monitoring, various physical property changes are employed to delineate the plume area and migration pathways with their pros and cons. We introduce a new rock physics model to facilitate the time-lapse estimation of CO2 saturation and possible pressure changes within a CO2 storage reservoir based on physical properties obtained from the prestack seismic inversion. We demonstrate that the CO2 plume delineation, saturation, and pressure changes estimations are possible using a combination of Acoustic Impedance (AI) and P- to S-wave velocity ratio (Vp/Vs) inverted from time-lapse or four-dimensional (4D) seismic. We assumed a scenario over a period of 40 years comprising an initial 25 year injection period. Our results show that monitoring the CO2 plume in terms of extent and saturation can be carried out using our rock physics-derived method. The suggested method, without going into the elastic moduli level, handles the elastic property cubes, which are commonly obtained from the prestack seismic inversion. Pressure changes quantification is also possible within un-cemented sands; however, the stress/cementation coefficient in our proposed model needs further study to relate that with effective stress in various types of sandstones. The three-dimensional (3D) seismic usually covers the area from the reservoir's base to the surface making it possible to detect the CO2 plume's lateral and vertical migration. However, the comparatively low resolution of seismic, the inversion uncertainties, lateral mineral, and shale property variations are some limitations, which warrant consideration. This method can also be applied for the exploration and monitoring of hydrocarbon production.

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.