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.

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.

Seismic Reflections of Rock Properties in a Clastic Environment

Generated by the propagation of sound waves, seismic reflections are essentially the reflections at the interface between various subsurface formations. Traditionally, these reflections are interpreted in a qualitative way by mapping subsurface geology without quantifying the rock properties inside the strata, namely the porosity, mineralogy, and pore fluid. This study aims to conduct the needed quantitative interpretation by the means of rock physics to establish the relation between rock elastic and petrophysical properties for reservoir characterization. We conduct rock physics diagnostics to find a theoretical rock physics model relevant to the data by examining the wireline data from a clastic depositional environment associated with a tight gas sandstone in the Continental US. First, we conduct the rock physics diagnostics by using theoretical fluid substitution to establish the relevant rock physics models. Once these models are determined, we theoretically vary the thickness of the intervals, the pore fluid, as well as the porosity and mineralogy to generate geologically plausible pseudo-scenarios. Finally, Zoeppritz (1919) equations are exploited to obtain the expected amplitude versus offset (AVO) and the gradient versus intercept curves of these scenarios. The relationship between elastic and petrophysical properties was established using forward seismic modeling. Several theoretical rock physics models, namely Raymer-Dvorkin, soft-sand, stiff-sand, and constant-cement models were applied to the wireline data under examination. The modeling assumes that only two minerals are present: quartz and clay. The appropriate rock physics model appears to be constant-cement model with a high coordination number. The result is a seismic reflection catalogue that can serve as a field guide for interpreting real seismic reflections, as well as to determine the seismic visibility of the variations in the reservoir geometry, the pore fluid, and the porosity. The obtained reservoir properties may be extrapolated to prospects away from the well control to consider certain what-if scenarios like plausible lithology or fluid variations. This enables building of a catalogue of synthetic seismic reflections of rock properties to be used by the interpreter as a field guide relating seismic data to volumetric reservoir properties.

Elastic anisotropy of shales: the role of crack alignment and compliance ratio

Cracks, broadly defined as compliant discontinuities, are a major cause of elastic anisotropy. However, few models are available for quantifying crack properties relevant to anisotropy. We developed a rock physics model to quantify crack angular distribution and normal-to-tangential compliance ratio from pressure-dependent acoustic velocities measured in the laboratory. The proposed model utilizes a rectangular function of variable width and amplitude to extract the maximum dip angle of cracks, which is a direct quantification of crack alignment relative to the bedding plane. We tested the model on an organic-rich shale dataset and confirm that both crack alignment and compliance ratio strongly impact Thomsen anisotropy parameters, thus demonstrating the model as a useful tool for better understanding how cracks affect elastic anisotropy.

Rock-physics machine learning toolkit for joint litho-fluid facies classification and compaction modeling

Correct lithofacies interpretation sourced from wireline log data is an essential source of prior information for joint seismic inversion for facies and impedances, among other applications. However, this information is difficult to interpret or extract manually due to the multivariate and high dimensionality of wireline logs. Facies inference is also challenging for traditional clustering-based approaches because pervasive compaction trends affect a number of petrophysical measurements simultaneously. Another common pitfall in automated clustering approaches is the inability to account for underlying diagenetic processes that correlate with depth. Here, we address these challenges by introducing a rock-physics machine learning toolkit for joint litho-fluid facies classification. The litho-fluid types are inferred from the borehole data within the objective framework of a maximum-likelihood approach for latent facies variables and rock-physics model parameters, explicitly accounting for compaction and depth effects. The inference boils down to an expectation-maximization (EM) algorithm with strong spatial coupling. Each litho-fluid type is associated with an instance of a particular rock-physics model with a unique set of fitting parameters, constrained to a physically reasonable range. These fitting parameters in turn are inferred using bound-constrained optimization as part of the EM algorithm. Outputs produced by the toolkit can be used directly to specify the necessary prior information for seismic inversion, including per-facies rock-physics models and facies proportions. We present an example application of the tool to real borehole data from the North West Shelf of Australia to illustrate the method and discuss its characteristic features in depth.

Porosity estimation based on rock skeleton general formula and comprehensive pore structure parameter – An application to a tight-sand reservoir

Most of current 3D reservoir’s porosity estimation methods are based on analyzing the elastic parameters inverted from seismic data. It is well-known that elastic parameters vary with pore structure parameters such as pore aspect ratio, consolidate coefficient, critical porosity, etc. Thus, we may obtain inaccurate 3D porosity estimation if the chosen rock physics model fails properly address the effects of pore structure parameters on the elastic parameters. However, most of current rock physics models only consider one pore structure parameter such as pore aspect ratio or consolidation coefficient. To consider the effect of multiple pore structure parameters on the elastic parameters, we propose a comprehensive pore structure (CPS) parameter set that is generalized from the current popular rock physics models. The new CPS set is based on the first order approximation of current rock physics models that consider the effect of pore aspect ratio on elastic parameters. The new CPS set can accurately simulate the behavior of current rock physics models that consider the effect of pore structure parameters on elastic parameters. To demonstrate the effectiveness of proposed parameters in porosity estimation, we use a theoretical model to demonstrate that the proposed CPS parameter set properly addresses the effect of pore aspect ratio on elastic parameters such as velocity and porosity. Then, we obtain a 3D porosity estimation for a tight sand reservoir by applying it seismic data. We also predict the porosity of the tight sand reservoir by using neural network algorithm and a rock physics model that is commonly used in porosity estimation. The comparison demonstrates that predicted porosity has higher correlation with the porosity logs at the blind well locations.

Multivariate probabilistic rock physics models using Kumaraswamy distributions

Rock physics models are physical equations that map petrophysical properties into geophysical variables, such as elastic properties and density. These equations are generally used in quantitative log and seismic interpretation to estimate the properties of interest from measured well logs and seismic data. Such models are generally calibrated using core samples and well log data and result in accurate predictions of the unknown properties. Because the input data are often affected by measurement errors, the model predictions are often uncertain. Instead of applying rock physics models to deterministic measurements, I propose to apply the models to the probability density function of the measurements. This approach has been previously adopted in literature using Gaussian distributions, but for petrophysical properties of porous rocks, such as volumetric fractions of solid and fluid components, the standard probabilistic formulation based on Gaussian assumptions is not applicable due to the bounded nature of the properties, the multimodality, and the non-symmetric behavior. The proposed approach is based on the Kumaraswamy probability density function for continuous random variables, which allows modeling double bounded non-symmetric distributions and is analytically tractable, unlike the Beta or Dirichtlet distributions. I present a probabilistic rock physics model applied to double bounded continuous random variables distributed according to a Kumaraswamy distribution and derive the analytical solution of the posterior distribution of the rock physics model predictions. The method is illustrated for three rock physics models: Raymer’s equation, Dvorkin’s stiff sand model, and Kuster-Toksoz inclusion model.

WELLSITE FULL WAVEFORM SONIC INTERPRETATION

Sonic data are now acquired in most wellbores for a variety of applications including seismic tie, porosity evaluation, lithology determination, fracture detection, gas detection, and geomechanics modeling. The industry is also more aware of the impacts of intrinsic (fractures, layering), extrinsic (stress), and borehole effects that may affect the basic measurements of compressional and shear slownesses. Any advanced interpretation of sonic data has historically been done days to weeks after the acquisition, and the value of the measurement can be diminished due to the time of delivery of the final product. An updated data-driven inversion algorithm applied while logging can provide robust shear and compressional slownesses with associated quality control indicators. The updated algorithm has fewer user parameters and is more reliable in layered, stressed, or damaged formations. Processing quality is determined using the coherency of the measured signal and an industry-standard rock physics model for theoretical validation. With the updated dipole shear inversion and more flexible dipole anisotropy frequency filters, the dipole shear anisotropy processing can deliver reliable results at the wellsite. A byproduct of the new dipole shear inversion algorithm is the environmental slowness that is used to optimally fit the dipole dispersion signal. The interpretation of the environmental slowness parameter can indicate the anisotropy mechanism in addition to zones of near-wellbore alteration to provide further insight immediately. The wellsite dipole shear inversion and anisotropy processing were run on a vertical well in eastern Australia, within a stacked tight gas sand reservoir that requires hydraulic fracturing. The main application of the sonic data was reliable slownesses as input to stress modeling for designing the stimulation, but the direction of the maximum horizontal stresses within the clastic gas-filled zones was also required. The dipole shear inversion results were able to handle various lithologies and hole conditions, as well as identify vertical transverse isotropy (VTI) anisotropic shale intervals between the horizontally stressed sand zones.