Summary
Accurate reservoir simulation requires data-rich geomodels. In this paper, geomodels integrate stochastic seismic inversion results (for means and variances of packages of meter-scale beds), geologic modeling (for a framework and priors), rock physics (to relate seismic to flow properties), and geostatistics (for spatially correlated variability). These elements are combined in a Bayesian framework. The proposed workflow produces models with plausible bedding geometries, where each geomodel agrees with seismic data to the level consistent with the signal-to-noise ratio of the inversion. An ensemble of subseismic models estimates the means and variances of properties throughout the flow simulation grid.
Grid geometries with possible pinchouts can be simulated using auxiliary variables in a Markov chain Monte Carlo (MCMC) method. Efficient implementations of this method require a posterior covariance matrix for layer thicknesses. Under assumptions that are not too restrictive, the inverse of the posterior covariance matrix can be approximated as a Toeplitz matrix, which makes the MCMC calculations efficient. The proposed method is examined using two-layer examples. Then, convergence is demonstrated for a synthetic 3D, 10,000 trace, 10 layer cornerpoint model. Performance is acceptable.
The Bayesian framework introduces plausible subseismic features into flow models, whilst avoiding overconstraining to seismic data, well data, or the conceptual geologic model. The methods outlined in this paper for honoring probabilistic constraints on total thickness are general, and need not be confined to thickness data obtained from seismic inversion: Any spatially dense estimates of total thickness and its variance can be used, or the truncated geostatistical model could be used without any dense constraints.
Introduction
Reservoir simulation models are constructed from sparse well data and dense seismic data, using geologic concepts to constrain stratigraphy and property variations. Reservoir models should integrate spare, precise well data and dense, imprecise seismic data.
Because of the sparseness of well data, stochastically inverted seismic data can improve estimates of reservoir geometry and average properties. Although seismic data are densely distributed compared to well data, they are uninformative about meter-scale features. Beds thinner than about 1/8 to 1/4 the dominant seismic wavelength cannot be resolved in seismic surveys (Dobrin and Savit 1988; Widess 1973). For depths of ˜3000 m, the maximum frequency in the signal is typically about 40 Hz, and for average velocities of ˜2,000 m/s, this translates to best resolutions of about 10 m. Besides the limited resolution, seismic-derived depths and thicknesses are uncertain because of noise in the seismic data and uncertainty in the rock physics models (Gunning and Glinsky 2004, 2006). This resolution limit and uncertainties associated with seismic depth and thickness estimates have commonly limited the use of seismic data to either inferring the external geometry or guiding modeling of plausible stratigraphic architectures of reservoirs (Deutsch et al. 1996).
In contrast, well data reveal fine-scale features but cannot specify interwell geometry. To build a consistent model, conceptual stacking and facies models must be constrained by well and seismic data. The resulting geomodels must be gridded for flow simulation using methods that describe stratal architecture flexibly and efficiently.
Approximate Bayesian inference of seismic velocity and pore-pressure uncertainty with basin modeling, rock physics, and imaging constraints