Statistical rock physics inversion of elastic and electrical properties for CO2 sequestration studies

2020 ◽  
Vol 223 (1) ◽  
pp. 707-724
Author(s):  
Mohit Ayani ◽  
Dario Grana
Keyword(s):  
Electrical Properties ◽  
Co2 Sequestration ◽  
Rock Physics ◽  
Real Data ◽  
Inversion Method ◽  
Model Parameters ◽  
The North ◽  
Physics Model ◽  
Rock Physics Model ◽  
Statistical Rock Physics

SUMMARY We present a statistical rock physics inversion of the elastic and electrical properties to estimate the petrophysical properties and quantify the associated uncertainty. The inversion method combines statistical rock physics modeling with Bayesian inverse theory. The model variables of interest are porosity and fluid saturations. The rock physics model includes the elastic and electrical components and can be applied to the results of seismic and electromagnetic inversion. To describe the non-Gaussian behaviour of the model properties, we adopt non-parametric probability density functions to sample multimodal and skewed distributions of the model variables. Different from machine learning approach, the proposed method is not completely data-driven but is based on a statistical rock physics model to link the model parameters to the data. The proposed method provides pointwise posterior distributions of the porosity and CO2 saturation along with the most-likely models and the associated uncertainty. The method is validated using synthetic and real data acquired for CO2 sequestration studies in different formations: the Rock Springs Uplift in Southwestern Wyoming and the Johansen formation in the North Sea, offshore Norway. The proposed approach is validated under different noise conditions and compared to traditional parametric approaches based on Gaussian assumptions. The results show that the proposed method provides an accurate inversion framework where instead of fitting the relationship between the model and the data, we account for the uncertainty in the rock physics model.

Hierarchical Bayesian lithology/fluid prediction: A North Sea case study

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. B69-B85 ◽  
Author(s):  
Kjartan Rimstad ◽  
Per Avseth ◽  
Henning Omre
Keyword(s):  
North Sea ◽  
Rock Physics ◽  
Model Parameters ◽  
Gas Oil ◽  
Clear Fluid ◽  
Prior Model ◽  
Spatial Coupling ◽  
The North ◽  
Likelihood Model ◽  
Physics Model

Seismic 3D amplitude variation with offset (AVO) data from the Alvheim field in the North Sea are inverted into lithology/fluid classes, elastic properties, and porosity. Lithology/fluid maps over hydrocarbon prospects provide more reliable estimates of gas/oil volumes and improve the decision concerning further reservoir assessments. The Alvheim field is of turbidite origin with complex sand-lobe geometry and appears without clear fluid contacts across the field. The inversion is phrased in a Bayesian setting. The likelihood model contains a convolutional, linearized seismic model and a rock-physics model that capture vertical trends due to increased sand compaction and possible cementation. The likelihood model contains several global model parameters that are considered to be stochastic to adapt the model to the field under study and to include model uncertainty in the uncertainty assessments. The prior model on the lithology/fluid classes is a Markov random field that captures local vertical/horizontal continuity and vertical sorting of fluids. The predictions based on the posterior model are validated by observations in five wells used as blind tests. Hydrocarbon volumes with reliable gas/oil distributions are predicted. The spatial coupling provided by the prior model is crucial for reliable predictions; without the coupling, hydrocarbon volumes are severely underestimated. Depth trends in the rock-physics likelihood model improve the gas versus oil predictions. The porosity predictions reproduce contrasts observed in the wells, and mean square error is reduced by one-third compared to Gauss-linear predictions.

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

2022 ◽  
Vol 9 ◽  
Author(s):  
Kyle T. Spikes ◽  
Mrinal K. Sen
Keyword(s):  
Reservoir Characterization ◽  
Rock Physics ◽  
Model Parameters ◽  
Data Sets ◽  
Unconsolidated Sands ◽  
Bayesian Formulation ◽  
Input Parameters ◽  
Physics Model ◽  
Rock Physics Model ◽  
Prior Models

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.

scholarly journals Rock physics model of glauconitic greensand from the North Sea

2010 ◽  
Author(s):  
Zakir Hossain ◽  
Tapan Mukerji ◽  
Jack Dvorkin ◽  
Ida L. Fabricius
Keyword(s):  
North Sea ◽  
Rock Physics ◽  
The North ◽  
The North Sea ◽  
Physics Model ◽  
Rock Physics Model

scholarly journals Bayesian Analysis to Determine Relative Significance of Inputs of a Rock-Physics Model

2021 ◽  
Vol 9 ◽  
Author(s):  
Kyle T. Spikes ◽  
Mrinal K. Sen
Keyword(s):  
Bayesian Analysis ◽  
Reservoir Characterization ◽  
Likelihood Function ◽  
Rock Physics ◽  
Rock Properties ◽  
Model Parameters ◽  
Prior Distributions ◽  
Relative Significance ◽  
Physics Model ◽  
Rock Physics Model

Rock-physics models relate rock properties to elastic properties through non-unique relationships and often in the presence of seismic data that contain significant noise. A set of inputs define the rock-physics model, and any errors in that model map directly into uncertainty in target seismic-scale amplitudes, velocities, or inverted impedances. An important aspect of using rock-physics models in this manner is to determine and understand the significance of the inputs into a rock-physics model under consideration. Such analysis enables the design of prior distributions that are informative within a reservoir-characterization formulation. We use the framework of Bayesian analysis to find internal dependencies and correlations among the inputs. This process requires the assignments of prior distributions, and calculation of the likelihood function, whose product is the posterior distribution. The data are well-log data that come from a hydrocarbon-bearing set of sands from the Gulf of Mexico. The rock-physics model selected is the soft-sand model, which is applicable to the data from the reservoir sands. Results from the Bayesian algorithm are multivariate histograms that demonstrate the most frequent values of the inputs given the data. Four analyses are applied to different subsets of the reservoir sands, and each reveals some correlations among certain model inputs. This quantitative approach points out the significance of a singular or joint set of rock-physics model parameters.

Multivariate probabilistic rock physics models using Kumaraswamy distributions

Geophysics ◽  
2021 ◽  
pp. 1-43
Author(s):  
Dario Grana
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Random Variables ◽  
Rock Physics ◽  
Petrophysical Properties ◽  
Kumaraswamy Distribution ◽  
Model Predictions ◽  
Physics Model ◽  
Rock Physics Model

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.

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

2021 ◽  
pp. 1-59
Author(s):  
Kai Lin ◽  
Xilei He ◽  
Bo Zhang ◽  
Xiaotao Wen ◽  
Zhenhua He ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Pore Structure ◽  
Seismic Data ◽  
Rock Physics ◽  
Structure Parameters ◽  
Pore Structure Parameter ◽  
Elastic Parameters ◽  
Physics Model ◽  
Rock Physics Model ◽  
Porosity Estimation

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.

scholarly journals The rock physics model in the unconsolidated methane hydrate bearing sediments

2010 ◽  
Vol 75 (1) ◽  
pp. 59-71 ◽  
Author(s):  
Takao Inamori ◽  
Masami Hato ◽  
Kiyofumi Suzuki ◽  
Tatsuo Saeki
Keyword(s):  
Methane Hydrate ◽  
Rock Physics ◽  
Physics Model ◽  
Rock Physics Model ◽  
Hydrate Bearing Sediments
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