Application of Bayesian Generative Adversarial Networks to Geological Facies Modeling

Mathematical Geosciences - Geological facies modeling is a key component in exploration and characterization of subsurface reservoirs. While traditional geostatistical approaches are still commonly...     

Constraining basin thermal history and petroleum generation using palaeoclimate data in the Piceance Basin,Colorado

Careful assessment of basin thermal history is critical to modelling petroleum generation in sedimentary basins. In this paper, we propose a novel approach to constraining basin thermal history using palaeoclimate temperature reconstructions and study its impact on estimating source rock maturation and hydrocarbon generation in a terrestrial sedimentary basin. We compile mean annual temperature (MAT) estimates from macroflora assemblage data to capture past surface temperature variation for the Piceance Basin, a high‐elevation, intermontane, sedimentary basin in Colorado, USA. We use macroflora assemblage data to constrain the temporal evolution of the upper thermal boundary condition and to capture the temperature change with basin uplift. We compare these results with the case where the upper thermal boundary condition is based solely upon a simplified latitudinal temperature estimate with no elevation effect. For illustrative purposes, 2 one‐dimensional (1‐D) basin models are constructed using these two different upper thermal boundary condition scenarios and additional geological and geochemical input data in order to investigate the impact of the upper thermal boundary condition on petroleum source rock maturation and kerogen transformation processes. The basin model predictions indicate that the source rock maturation is very sensitive to the upper thermal boundary condition for terrestrial basins with variable elevation histories. The models show substantial differences in source rock maturation histories and kerogen transformation ratio over geologic time. Vitrinite reflectance decreases by 0.21%Ro, source rock transformation ratio decreases 10.5% and hydrocarbon mass generation decreases by 16% using the macroflora assemblage data. In addition, we find that by using the macroflora assemblage data, the modelled depth profiles of vitrinite reflectance better matches present‐day measurements. These differences demonstrate the importance of constraining thermal boundary conditions, which can be addressed by palaeotemperature reconstructions from palaeoclimate and palaeo‐elevation data for many terrestrial basins. Although the palaeotemperature reconstruction compiled for this study is region specific, the approach presented here is generally applicable for other terrestrial basin settings, particularly basins which have undergone substantial subaerial elevation change over time.     

Regularized sparse‐grid geometric sampling for uncertainty analysis in non‐linear inverse problems

This paper introduces an efficiency improvement to the sparse‐grid geometric sampling methodology for assessing uncertainty in non‐linear geophysical inverse problems. Traditional sparse‐grid geometric sampling works by sampling in a reduced‐dimension parameter space bounded by a feasible polytope, e.g., a generalization of a polygon to dimension above two. The feasible polytope is approximated by a hypercube. When the polytope is very irregular, the hypercube can be a poor approximation leading to computational inefficiency in sampling. We show how the polytope can be regularized using a rotation and scaling based on principal component analysis. This simple regularization helps to increase the efficiency of the sampling and by extension the computational complexity of the uncertainty solution. We demonstrate this on two synthetic 1D examples related to controlled‐source electromagnetic and amplitude versus offset inversion. The results show an improvement of about 50% in the performance of the proposed methodology when compared with the traditional one. However, as the amplitude versus offset example shows, the differences in the efficiency of the proposed methodology are very likely to be dependent on the shape and complexity of the original polytope. However, it is necessary to pursue further investigations on the regularization of the original polytope in order to fully understand when a simple regularization step based on rotation and scaling is enough.     

Scale Matching with Factorial Kriging for Improved Porosity Estimation from Seismic Data

When seismic data and porosity well logs contain information at different spatial scales, it is important to do a scale-matching of the datasets. Combining different data types with scale mismatch can lead to suboptimal results. A good correlation between seismic velocity and rock properties provides a basis for integrating seismic data in the estimation of petrophysical properties. Three-dimensional seismic data provides an unique exhaustive coverage of the interwell reservoir region not available from well data. However, because of the limitations of measurement frequency bandwidth and view angles, the seismic image can not capture the true seismic velocity at all spatial scales present in the earth. The small-scale spatial structure of heterogeneities may be absent in the measured seismic data. In order to take best advantage of the seismic data, factorial kriging is applied to separate the small and large-scale structures of both porosity and seismic data. Then the spatial structures in seismic data which are poorly correlated with porosity are filtered out prior to integrating seismic data into porosity estimation.     

Elastic behaviour of North Sea chalk: A well-log study

We present two different elastic models for, respectively, cemented and uncemented North Sea chalk well‐log data. We find that low Biot coefficients correlate with anomalously low cementation factors from resistivity measurements at low porosity and we interpret this as an indication of cementation. In contrast, higher Biot coefficients and correspondingly higher cementation factors characterize uncemented chalk for the same (low) porosity. Accordingly, the Poisson's ratio–porosity relationship for cemented chalk is different from that of uncemented chalk. We have tested the application of the self‐consistent approximation, which here represents the unrelaxed scenario where the pore spaces of the rock are assumed to be isolated, and the Gassmann theory, which assumes that pore spaces are connected, as tools for predicting the effect of hydrocarbons from the elastic properties of brine‐saturated North Sea reservoir chalk. In the acoustic impedance–Poisson's ratio plane, we forecast variations in porosity and hydrocarbon saturation from their influence on the elastic behaviour of the chalk. The Gassmann model and the self‐consistent approximation give roughly similar predictions of the effect of fluid on acoustic impedance and Poisson's ratio, but we find that the high‐frequency self‐consistent approach gives a somewhat smaller predicted fluid‐saturation effect on Poisson's ratio than the low‐frequency Gassmann model. The Gassmann prediction for the near and potentially invaded zone corresponds more closely to logging data than the Gassmann prediction for the far, virgin zone. We thus conclude that the Gassmann approach predicts hydrocarbons accurately in chalk in the sonic‐frequency domain, but the fluid effects as recorded by the acoustic tool are significantly affected by invasion of mud filtrate. The amplitude‐versus‐angle (AVA) response for the general North Sea sequence of shale overlying chalk is predicted as a function of porosity and pore‐fill. The AVA response of both cemented and uncemented chalk generally shows a declining reflectivity coefficient versus offset and a decreasing normal‐incidence reflectivity with increasing porosity. However, for the uncemented model, a phase reversal will appear at a relatively lower porosity compared to the cemented model.     

The Value of Information in Spatial Decision Making

Experiments performed over spatially correlated domains, if poorly chosen, may not be worth their cost of acquisition. In this paper, we integrate the decision-analytic notion of value of information with spatial statistical models. We formulate methods to evaluate monetary values associated with experiments performed in the spatial decision making context, including the prior value, the value of perfect information, and the value of the experiment, providing imperfect information. The prior for the spatial distinction of interest is assumed to be a categorical Markov random field whereas the likelihood distribution can take any form depending on the experiment under consideration. We demonstrate how to efficiently compute the value of an experiment for Markov random fields of moderate size, with the aid of two examples. The first is a motivating example with presence-absence data, while the second application is inspired by seismic exploration in the petroleum industry. We discuss insights from the two examples, relating the value of an experiment with its accuracy, the cost and revenue from downstream decisions, and the design of the experiment.     

Constraints on velocity-depth trends from rock physics models

Estimates of depth, overpressure and amount of exhumation based on sonic data for a sedimentary formation rely on identification of a normal velocity–depth trend for the formation. Such trends describe how sonic velocity increases with depth in relatively homogeneous, brine‐saturated sedimentary formations as porosity is reduced during normal compaction (mechanical and chemical). Compaction is ‘normal’ when the fluid pressure is hydrostatic and the thickness of the overburden has not been reduced by exhumation. We suggest that normal porosity at the surface for a given lithology should be constrained by its critical porosity, i.e. the porosity limit above which a particular sediment exists only as a suspension. Consequently, normal velocity at the surface of unconsolidated sediments saturated with brine approaches the velocity of the sediment in suspension. Furthermore, porosity must approach zero at infinite depth, so the velocity approaches the matrix velocity of the rock and the velocity–depth gradient approaches zero. For sediments with initially good grain contact (when porosity is just below the critical porosity), the velocity gradient decreases with depth. By contrast, initially compliant sediments may have a maximum velocity gradient at some depth if we assume that porosity decreases exponentially with depth. We have used published velocity–porosity–depth relationships to formulate normal velocity–depth trends for consolidated sandstone with varying clay content and for marine shale dominated by smectite/illite. The first relationship is based on a modified Voigt trend (porosity scaled by critical porosity) and the second is based on a modified time‐average equation. Baselines for sandstone and shale in the North Sea agree with the established constraints and the shale trend can be applied to predict overpressure. A normal velocity–depth trend for a formation cannot be expressed from an arbitrary choice of mathematical functions and regression parameters, but should be considered as a physical model linked to the velocity–porosity transforms developed in rock physics.     

Vp‐Vs relationship and amplitude variation with offset modelling of glauconitic greensand‡

The relationship between V_p and V_s may be used to predict V_s where only V_p is known. V_p/V_s is also used to identify pore fluids from seismic data and amplitude variation with offset analysis. Theoretical, physical, as well as statistical empirical V_p‐V_s relationships have been proposed for reservoir characterization when shear‐wave data are not available. In published work, the focus is primarily on the V_p‐V_s relationship of quartzitic sandstone. In order to broaden the picture we present V_p‐V_s relationships of greensand composed of quartz and glauconite by using data from the Paleocene greensand Nini oil field in the North Sea. A V_p‐V_s relationship derived from modelling is compared with empirical V_p‐V_s regressions from laboratory data as well as from log data. The accuracy of V_s prediction is quantified in terms of root‐mean‐square error. We find that the V_p‐V_s relationship derived from modelling works well for greensand shear‐wave velocity prediction. We model the seismic response of glauconitic greensand by using laboratory data from the Nini field. Our studies here reveal that brine‐saturated glauconitic greensand can have a similar seismic response to that from oil‐saturated quartzitic sandstone and that oil‐saturated strongly cemented greensand can have a similar amplitude variation with offset response to that from brine‐saturated weakly cemented greensand.