Effects of uncertainty in rock‐physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlled‐source electromagnetics data

Abstract

A B S T R A C TThis paper investigates the effects of uncertainty in rock-physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlledsource electromagnetics data. The reservoir parameters are related to electrical resistivity by the Poupon model and to elastic moduli and density by the Xu-White model. To handle uncertainty in the rock-physics models, we consider their outputs to be random functions with modes or means given by the predictions of those rock-physics models and we consider the parameters of the rock-physics models to be random variables defined by specified probability distributions. Using a Bayesian framework and Markov Chain Monte Carlo sampling methods, we are able to obtain estimates of reservoir parameters and information on the uncertainty in the estimation. The developed method is applied to a synthetic case study based on a layered reservoir model and the results show that uncertainty in both rock-physics models and in their parameters may have significant effects on reservoir parameter estimation. When the biases in rock-physics models and in their associated parameters are unknown, conventional joint inversion approaches, which consider rock-physics models as deterministic functions and the model parameters as fixed values, may produce misleading results. The developed stochastic method in this study provides an integrated approach for quantifying how uncertainty and biases in rock-physics models and in their associated parameters affect the estimates of reservoir parameters and therefore is a more robust method for reservoir parameter estimation. I N T R O D U C T I O NRock-physics models are needed for reservoir parameter estimation using seismic amplitude variation with angle (AVA) and controlled-source electromagnetics (CSEM) data. In practice, these models are often derived from suitable nearby borehole logs. Firstly, appropriate families of rock-physics models are chosen. For instance, we may choose a sand-clay model by Dvorkin and Nur (1996), the Xu-White model by Xu and White (1995) or a differential effective medium model by * (1985) and Mavko, Mukerji and Dvorkin (1998) for seismic AVA data and we may choose Archie's law (Archie 1942) or the Poupon model (Poupon, Loy and Tixier 1954;Poupon and Leveaux 1971) for CSEM data. NorrisSecondly, the parameters in the chosen rock-physics models are estimated by fitting them to the selected borehole logs. Since relationships between the reservoir parameters and the geophysical attributes are often nonlinear and non-unique, the derived rock-physics models are inevitably subject to uncertainty and even unknown biases. These may include uncertainty and biases due to an inappropriate choice of the rockphysics model families and those due to inaccurate estimation of the associated model parameters.

Background resistivity model from seismic velocities

“…These errors are likely to be bigger than the errors in the data themselves, as Myoung and Snieder (2011) show. We adapt the methodology of Chen and Dickens (2009), who emphasize that parameter uncertainty and model uncertainty have to be taken into account.…”

“…That means that any of these methods can introduce unwanted bias. Chen and Dickens (2009) look at the effects of uncertainty involved in the rock physics model itself (intrinsic) and their parameters (extrinsic), and Myoung and Snieder (2011) show that the uncertainty of the rock physics model contributes more to the overall uncertainty than the uncertainty in the data themselves.…”

“…Other parameters are either constant or a linear function of depth. Finally, we use Chen and Dickens (2009) to estimate the related uncertainty. The result is a transform that can be applied to seismic velocities to get background resistivities.…”

Assessing the monitorability of CO2 saturation in subsurface saline aquifers

“…We use a Monte Carlo inversion approach to describe reservoir parameters and their associated uncertainties (e.g., Bachrach, 2006;Larsen et al, 2006;Spikes et al, 2007;Bosch et al, 2007;Chen and Dickens, 2009). To quantify the information content of the so-called posterior probability distributions, we use Shannon's entropy (Shannon, 1948), which is an appropriate single parameter to describe probability distributions even when they are multimodal or highly skewed.…”

Seismic inversion and uncertainty analysis using a transdimensional Markov chain Monte Carlo method

“…The uncertainty in geophysical inverse problems was estimated by various stochastic inversion algorithms, such as MCMC (Liu and Stock, 1993;Malinverno and Briggs, 2004;Chen and Dickens, 2009;Gunning et al, 2010;Kwon and Snieder, 2011), SA (Dosso, 2002;Dosso and Nielsen, 2002;Bhattacharya et al, 2003;Roy et al, 2005;Varela et al, 2006), PSO (Fernández-Martínez et al, 2012;Rumpf and Tronicke, 2015), and rjMCMC Reading and Gallagher, 2013;Dadi, 2014;Galetti et al, 2015;Dadi et al, 2015).…”