Whitcombe (2002) was largely driven by the fact that it was based on the 2-term Aki-Richards approximation to the. Zoeppritz equations (Aki & Richards, 1980), ...
Lithology constrained elastic inversion – application to Niobrara brittleness
Lithology constrained elastic inversion – Application to Niobrara brittleness estimation Yacine Kiche, Lyes Ouhib, GO Geoengineering, Dave Balogh* and Ahmed Ouenes, FracGeo Summary Elastic inversion is a geophysical process used to recover the constituent rock properties of the earth and is a critical component for the development of unconventional reservoirs, but suffers from challenges related to the sensitivity of the inverse problem to noise and to the sheer number of possible earth models. An elastic inversion workflow based on the elastic impedance concept is introduced. The new workflow utilizes well log-derived rock physics relationships defined for each facies and a lithology/facies model to highly constrain the inversion space, thereby reducing inversion run-time and regularizing the problem in the presence of noise while providing geologically sound elastic properties. The inversion workflow is illustrated on the Niobrara formation where the Brittleness defined by combining Young Modulus and Poisson’s Ratio allows the identification of the best hydraulic fracturing areas. Introduction Elastic inversion is the process by which variations in the amplitude of seismic signals with incidence angle allow for the fundamental rock properties of an earth model (VP, VS, and density) to be recovered. The implications of AVO/AVA effects to seismic exploration were first recognized as direct hydrocarbon indicator nearly 36 years ago, initially as a function of offset (Ostrander, 1980). The concept of AVO was quickly adapted to determining additional elastic parameters, such as Poisson’s ratio (Balogh et.al., 1986), to aid in delineating stratigraphic variations and fluid composition. Recently, the ability of elastic inversion to predict the general magnitude and variations of local stress trends (Goodway et al., 2010) as well as directly calculate geomechanical and reservoir engineering properties of interest such as Rickman Brittleness (Gray et al., 2012) has caused elastic inversion (EI) to become a critical component in modern unconventional reservoir characterization (Ouenes, 2012). EI, based on the 3-term Aki-Richard's equation, was derived by Connolly(1999), is shown by: ( )= = 1 + tan
Where: ,
= −8 , = 1 − 4 ,
=
The decision to use this formulation of the normalized elastic impedance in lieu of the one explicitly stated by Whitcombe (2002) was largely driven by the fact that it
was based on the 2-term Aki-Richards approximation to the Zoeppritz equations (Aki & Richards, 1980), and as such is limited in accuracy to angles less than 30°. Given the realities of modern seismic acquisition, where reservoirdepth reflection angles at and greater than 30° are routinely recorded, the far offset elastic impedance values introducing a significant amount of systematic error to the inversion. Based on empirical observations, this systematic error will typically result in overestimated velocity values and underestimated density values. In contrast, the 3-term Aki-Richards linearization is generally considered to be accurate up to the critical angle, and therefore would allow for the far stack impedances to contribute to an accurate inversion result. This is particularly important because the far angle data provides the greatest theoretical variation in amplitude, and therefore reduces the inherent ambiguity in the derived results. A more subtle advantage of the three term formulation lies in the increased variability of impedance values given a certain subset of input parameters, particularly at angles greater than 20°. This increased variability means that the inversion will have reduced ambiguity with regards to the model results, and implicitly results in an improved parameter resolution. A major challenge to elastic inversion lies in its’ sensitivity to noise. In the absence of noise, the elastic inversion will correctly fit the elastic impedances to the real rock properties in the subsurface (within the small error margins due to the linearized approximation mentioned above). However, the addition of a very small amount of noise to the data can dramatically change the resultant rock properties. This means that an unconstrained inversion, especially in land surveys where the S/N ratio is lower, will generally produce inconsistent and erroneous values. These issues point to the need to constrain the inversion to geologic information. Constraining the inversion with lithology/facies driven rock physics While todays unconventional reservoirs generally do not enjoy the exceptional S/N ratio that offshore surveys do, they typically do enjoy the advantage of extensive well control. In particular, the prevalence of sonic and density logs allow for empirical, facies-specific rock physics relationships between VP, VS, and ρ to be quickly and accurately determined. One can utilize these relationships to obtain an initial model fit to the seismic data, varying only the VP until a minima on the trend line is reached. This initial model fitting has the effect of greatly reducing inversion run time, regularizing the inverse problem in the presence of noise, and ensuring that the inversion results
Rock physics-constrained elastic inversion
honor the log data including the facies. Once an initial fit for the model had been achieved, a second stage of model fitting occurs utilizing traditional misfit optimization methods within a model space constrained by an ellipsoid of the standard deviation of VP and the conditional deviations of VS and ρ to VP within the log data, allowing the model to iterate towards a best fit solution, while still honoring the log data and the corresponding facies. In practice, this means that very homogenous sequences will be very highly constrained, while more heterogeneous areas will showcase the variability of the geology. For this particular workflow, the Krief relation and a generalized Gardner’s relation were utilized for each facies to control the initial model fitting, given as: =
)∙
( (
and
=
)
Where VFl is the velocity of the pore fluid, VLith is the fractional velocity average of the specific mineralogy of the formation in question. Using the generalized form of these equations gives the user great flexibility to incorporate all meaningful local log data and facies knowledge available into the inversion.
The importance of the facies/lithology could be seen when plotting the Young Modulus (Fig. 1A) and Poisson’s Ratio (Fig. 1B) versus the Gamma Ray log. These elastic properties depend heavily on the mineralogy which is very often highly correlated with the GR log. Unlike previous efforts using the Extended EI (Kim et al, 2015) where the goal was to derive a good prediction of the elastic properties from the seismic, in this work we add the facies constraint which needs to be consistent with the derived elastic properties while reducing dramatically the noise seen in previous results (Kim et al. 2015). Given the importance of Gamma Ray log (GR) in unconventional reservoirs, we use this widely available log to define three facies: Facies 1 for GR < 100, Facies 2 for 100
