Direct Probabilistic Anisotropic AVO Inversion to correctly populate Geomechanical model uncertainty in shales and tight reservoirs

Bill Goodway, Raul Cova, Evan Mutual, Andrew Mills, Adriana Gordon, Wendell Pardasie; Qeye Labs.

Marco Perez, Andrew Iverson; Velvet Energy.

Abstract

Within the application of seismic reservoir characterization to unconventional tight formations, there is a need to improve and, in many cases, correct the standard underdetermined AVO inversion estimates of key seismic petrophysical parameters (rock properties) that control hydro-frac stimulation, such as the heterogeneity of rock quality (e.g. mineralogic brittleness, porosity, TOC), natural fractures and in-situ stress. Furthermore, reservoir characterization related decision-making for horizontal well placement and risk analysis, also requires an increasing degree of assessment of the uncertainties associated with any predictions based on seismic Quantitative Interpretation (QI). Bayesian inference solutions provide a framework where these issues can be addressed. However, in its standard formulation and given the size of typical seismic volumes, it might be computationally prohibitive. In this study we show how, under reasonable assumptions, a high dimensional Bayesian inference problem can be reduced to several local low dimensional inference problems, reducing the computational cost of this solution. This enables the application of a general and flexible probabilistic framework for rigorous propagation of uncertainties where prior knowledge from multiple anisotropic elastic and lithofacies domains can be easily integrated with the resulting uplift in resolution to resolve ambiguities and errors inherent in standard deterministic AVO/QI inversion. This approach was tested, on the local scale inference problem of estimating the following components involved in seismic reservoir characterization of unconventional tight formations:

1. VTI impact on AVO, with isotropic AVO fit showing the effects of overlying shale VTI on target tight gas resource zone’s i.e., decreasing Poisson ratio with increasing Young’s modulus for near constant Acoustic P-Impedance (AI), that guarantees a false positive Brittleness in the underlying target zone from standard deterministic AVO/QI inversion anisotropic overprint of isotropic estimates

2. Ambiguous Elastic Lithofacies: Lithology and mineralogic mixtures (sand, shale, carbonate…)

3. Fractures and effective porosity 4. Kerogen and fluids in non-equant porosity 5. Horizontal Stress Anisotropy (due to tectonic stresses) from Azimuthal Amplitude Versus

Offset (AVAZ) inversion for anisotropic elastic parameters and overprint of isotropic estimates

The results from implementing this Direct Probabilistic Anisotropic AVO Inversion will illustrate the method’s ability to provide robust estimates of these components at and below seismic tuning due to the utilization of statistical prior information. The approach will be applied for a better, correct seismic reservoir characterization of key geologic and reservoir parameters in unconventional tight formations, that will be estimated from the integration of data and information from different domains such as sonic scanner well logs, anisotropic rock physics, seismic data and geological facies.

Ambiguities and false positive rock properties from seismic AVO inversion

Understanding the anisotropic component of point 1) from the previous section, demonstrates one aspect of standard deterministic AVO inversion being unable to correctly estimate subsurface rock properties in the presence of background VTI shales. Figures 1 a, b), 2), and 3), show how the model of the observed VTI AVO response is fitted by an isotropic AVO curve thereby compounding the overlying shale’s false positive effects with the estimate of the underlying tight gas elastic properties. The result (see Figure 3) guarantees an incorrect Brittleness Vp/Vsv estimate from a near constant AI with decreasing Poisson’s ratio and increasing Young’s modulus, from standard deterministic AVO inversion.

Figure 1a) Parameters used in model of VTI shale overlying tight gas shale reservoir.

Figure 2) Observed VTI Ruger AVO fitted with an isotropic AVO curve showing the false positive effects of overlying shale VTI.

Figure 1b) VTI Vp/Vs increase (from Vp and Vsv) with angle in overlying shale layer produces a relative Vp/Vs decrease for constant AI in the underlying layer of quartz rich tight gas shale reservoir.

VTI Shale: Vp 3797m/s, Vs 1864m/s, Rho 2.66g/cc, e=0.12, d=0.1

Tight Gas: Vp 4233m/s, Vs 2544m/s, Rho 2.55g/cc, e=0.0, d=0.0

Shale

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260027002800290030003100320033003400350036003700380039004000410042004300440045004600470048004900500051005200530054005500560057005800590060006100620063006400

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P-P refelctivity v's Avg. Angle using VpVsRho input (from Aki & Richards approximation)VTI Ruger AVO and Thomsen VTI shale Vp/Vs with angle

Rp isotropic shale-sand Rp Ruger VTI shale Rp iso shale-sand fit to VTI Ruger

Figure 3) Effects of overlying VTI shale imprint on deterministic AVO guarantees a false positive Brittleness trend in underlying tight gas shale reservoir target. Compare trends (black-red arrows) for “Brittle” and “False overlying Shale VTI imprint”.

Beyond the overlying VTI shale problem, standard underdetermined deterministic AVO inversion is unable to differentiate the many complex yet similar elastic responses of overlapping rock properties for various lithologies and fluid configurations. This is an intrinsic characteristic of the underdetermined non-uniqueness of the inversion problem that can be mitigated by integrating relevant and non-redundant information into the inversion process. Standard inversion techniques for example, are “unaware” of the lithological deposition, bed thickness distributions and petrophysical relationships such lithofacies, effective fracture porosity, kerogen and fluid fill in non-equant porosity within the zone of interest as shown schematically in the following Figures: 4), 5), and 6).

Figure 4. Complex hierarchy of unconventional rock physics classification for model-based relationships.

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actual sand Sand AVO fit to VTI shale/sand

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Lines of constant Youngs Modulus (curved), Poisson Ratio (radial), P-wave Modulus (sloping) with Grigg-Barnett brittleness trend (dashed) on Lambda vs. Mu crossplot

UNCONVENTIONAL ROCK PHYSICS MODEL

Inorganic Material Organic Material

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C33 = 9.8 GPaC44 = 3.2 GPa

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Figure 5. LambdaRho vs. MuRho cross-plot of elastic property models of rock physics that provide prior information templates describing mineralogy, fluid, pore shape and kerogen.

Figure 6. LambdaRho vs. MuRho template showing the combined rock physics model for isotropic and anisotropic effects that introduce additional elastic parameter ambiguity and overprint causing a scatter in the model template cross-plot.

The additional required information is readily available from sonic scanner well logs, core and geological studies that provide a model for specific ranges of elastic properties for target zone facies, average thicknesses and their petrophysical variation, stratigraphic position within a formation, as well as the presence of gas, oil, or kerogen content. Defining a set of rules based on this information will reduce the solution space dramatically. However, in conventional deterministic seismic inversion algorithms all this information is difficult or unfeasible to integrate. Moreover, the correct propagation of uncertainties through the inversion is not possible. The study will present an integration example, where information from standard processed seismic AVO data are integrated with information from a range of other domains from different domains such as well logs, seismic data and geology, as described above. We show how this approach can help the QI involved in unconventional reservoir characterization by improving the accuracy and detail in the estimation of key rock physics (seismic petrophysics) parameters that control hydro-frac stimulation, such as the heterogeneity of rock quality (e.g. mineralogic brittleness, porosity, kerogen-TOC), natural fractures and in-situ stress.

ELASTIC PROPERTIES OF ROCKS

Porosity: φ

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φ = spherical pores φ = cracksφ = 0

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Can build templates that describes mineralogy, fluid, pore shape and kerogen

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Estimating the Presence of Kerogen

Anisotropic LMR cross-plot:Plotted as the c13 (l13) andc44 (m44 weak) components of the stiffness tensor

Colored dots represent the elastic

parameters from log based gas shale

zone color coded by volume of TOC

Black dots are the samples that

correspond to a narrow range of quartz content (47.5 – 52.5%)

Blue line with dots is the intrinsic VTI anisotropic trend line for this specific

mineral quantity-each white dot represents a 10% increase in TOC

The blue line with squares accounts for the presence of cracks, it helps explain

the scatter seen in the cross-plot

(theoretical derivation by Marco Perez)c13 [GPa g/cc]

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Fine tune model by:

Adding cracksAdding intrinsic VTI anisotropy

Vol Quartz: 0.475 – 0.525

10% increase in Vol TOC

10% increase in crack density

Vol TOC

Direct Probabilistic Inversion (DPI)

The general underlying DPI approach, consists of a one-step inversion process, based on the Bayesian probabilistic formulation introduced by Jullum and Kolbjørnsen (2016). This approach honours multi domain inputs and assumptions, respecting the confidence range in these inputs. A key attribute of DPI is that the geological framework of prior information can be encoded and combined with seismic AVO modelling to provide reliable results. This geological framework might include geological and petrophysical relationships such as encasing VTI shale facies, lithofacies with effective fracture porosity, kerogen and fluid fill in non-equant porosity, elastic property ranges and intra property and distance correlations for each facies. The prior information including a number of elastic property relationships/models can be broad and plausible but also very strict/narrow depending on the level of available knowledge. Handling the spatial information enables an optimal propagation of uncertainty and handles the non-uniqueness of the problem by providing probabilities. Under some conditions the reduction of the solution space allows DPI to resolve features below seismic resolution. The result of the DPI is a probability volume for each of the defined geological facies and anisotropic petrophysical parameters including natural fractures and in-situ stress. Furthermore, many other properties can be derived from having the probability for each facies. For example, all the facies’ elastic parameter probabilities can be combined using the full AVO signal and the geological information into the most likely facies and corresponding probability. Finally, by integrating all these probabilities a volume of high resolution sub-tuning intervals is produced.

Figure 7. Schematic workflow for the stochastic QI DPI method.

An example of this workflow for unconventional reservoirs, is demonstrated by a synthetic model-based application of isotropic compared to anisotropic DPI as shown in Figures: 8), 9), and 10), where the resulting statistical fidelity for estimates of elastic properties are: Isotropic DPI:

• Fraction AI within 2 stds: 0.86 • Fraction Vp/Vs within 2 stds: 0.92 • Fraction density within 2 stds: 0.71 • Correct facies classification in trace 0: 29.84%

Anisotropic VTI DPI: • Fraction AI within 2 stds: 0.97 • Fraction Vp/Vs within 2 stds: 0.97 • Fraction density within 2 stds: 0.96 • Fraction epsilon within 2 stds: 0.96 • Fraction delta within 2 stds: 0.93 • Correct facies classification in trace 0: 91.31%

Sampling

Localise

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neighbourhood

posterior

priorlikelihood

Figure 8. Synthetic model anisotropic elastic parameters: Vp/Vs vs AI, AI vs Rho, Vp/Vs vs Rho and Epsilon vs Delta (Thomsen VTI parameters).

Figure 9. Isotropic DPI (anisotropic input data) Observations:

• Large residuals • Poor accuracy differentiating siltstones from shales

Figure 10. VTI DPI (anisotropic input data) Observations:

• Small residuals • Better certainty in classification of shales and siltstones

Conclusions

Under reasonable assumptions, a high dimensional Bayesian inference problem can be reduced to several local low dimensional inference problems. This enables an application of a general and flexible probabilistic framework for rigorous propagation of uncertainties and for integrating prior knowledge from multiple domains. Moreover, this approach renders the Bayesian inversion a computationally affordable solution for industry sized AVO seismic volumes. The results of this study will illustrate the ability of this method to provide probabilistic volumes of lithofacies (sand, shale variability, carbonate…), fractures and effective porosity, kerogen and fluids in non-equant porosity and Horizontal Stress Anisotropy due to tectonic stresses for anisotropic elastic parameters that overprint isotropic estimates, at and below seismic tuning due to the utilization of statistical prior information.

Acknowledgements

The authors would like to thank Velvet Energy for permission to use and publish the data.

References

Hansen, H. J., Jakobsen A. F., Jollands A., and Nicholson F. [2018] Local Probabilistic Inversion of seismic AVO data. EAGE Annual Conference Abstracts. Jullum, M., Kolbjørnsen, O., [2016] A Gaussian-based framework for local Bayesian inversion of geophysical data to rock properties. Geophysics. Volume 81. No 3. 1-13. Larsen, A. L., Ulvmoen M., Omre H., and Buland A., [2006] Bayesian lithology/fluid prediction and simulation on the basis of a Markov-chain prior model. Geophysics. Volume 71. No. 5. R69–R78. Tarantola, A. [2005] Inverse Problem Theory and Methods for Model Parameter Estimation. Society for Industrial and Applied Mathematics (SIAM).