Bayesian inversion of 4D seismic data to pressure and saturation changes: Application to a west of Shetlands field

Abstract

A Bayesian inversion methodology is proposed that inverts angle-stacked 4D seismic maps to changes in pressure, water saturation and gas saturation. The inversion method is applied to data from a siliciclastic reservoir in the west of Shetlands, UK continental shelf. We present inversion results for three seismic monitor surveys and demonstrate the added value of pressure-saturation inversion by providing insights into reservoir connectivity and fluid dynamics across 14 years of reservoir production. In these surveys, 4D seismic signals related to waterflood, pressure increase and depletion, and gas exsolution are evident and overlap each other in many regions. To regularize this ill-posed inversion problem, we propose a Bayesian formulation that incorporates spatially variant prior information derived from a history-matched reservoir simulation model and well pressure measurements. The benefit of incorporating these multi-disciplinary data as prior information is demonstrated by comparing to inversion results using a spatially invariant prior. We show that the method takes advantage of the multi-disciplinary prior information to make more precise inferences where the seismic data are most uncertain. This leads to more realistic spatial distributions for the pressure and water-saturation inversion results. The non-uniqueness in this non-linear inversion is studied by analysing uncertainty estimates produced by stochastic sampling of the Bayesian posterior distribution. Posterior standard deviations are observed to be related to the sensitivity of the seismic amplitudes to the changes in each dynamic property as well as the degree of overlap between changes in different dynamic properties. Estimated pressure increases have a posterior standard deviation of approximately 1 MPa, whereas posterior standard deviations for pressure decrease are on average 4 MPa, with higher values applicable to regions of gas exsolution. The posterior standard deviation for estimates of gas saturation change is 0.07 for moderate, visible saturation signals, but 0.005 for low-to-zero gas saturation change. The posterior standard deviation for estimated water saturation change is mainly influenced by overlapping changes in pressure and gas saturation. When water changes dominate the 4D seismic signal, posterior standard deviations are on average 0.05. These values rise to 0.25 in areas where the water change is obscured by pressure or gas-saturation changes.

Multi-ensemble Bayesian Analysis of Inclusion-based Rock-physics Models

“…Deterministic or probabilistic approaches can be used to solve geophysical inverse problems 9,10,11,12,13 . The Bayesian framework is particularly conducive to solving seismic and rockphysics inversion problems in a probabilistic fashion 7,14,15,16,17,18,19,20,21 . In this type of formulation, the user provides geological knowledge as the prior and the likelihood function to compute the probability density functions of the underlying model inputs.…”