This paper considers Bayesian methods to discriminate between models depending on posterior model probability. When applying ensemble-based methods for model updating or history matching, the uncertainties in the parameters are typically assumed to be univariate Gaussian random fields. In reality, however, there often might be several alternative scenarios that are possible a priori. We take that into account by applying the concepts of model likelihood and model probability and suggest a method that uses importance sampling to estimate these quantities from the prior and posterior ensembles. In particular, we focus on the problem of conditioning a dynamic reservoir-simulation model to frequent 4D-seismic data (e.g., permanent-reservoir-monitoring data) by tuning the top reservoir surface given several alternative prior interpretations with uncertainty. However, the methodology can easily be applied to similar problems, such as fault location and reservoir compartmentalization. Although the estimated posterior model probabilities will be uncertain, the ranking of models according to estimated probabilities appears to be quite robust.
We consider the problem of identifying geothermal reservoirs in an exploration setting utilizing information from transient electromagnetic (TEM) and magnetotelluric (MT) data. The inversion methodology proposed uses information about the conductive clay cap gained from TEM inversion in the generation of a prior model for Bayesian inversion of 3D MT data. To facilitate the identification of large-scale structures typically associated with geothermal exploration, a level-set type representation of the electric resistivity is utilized. TheMTinversion is performed using the ensemble Kalman filter, which does not require calculation of sensitivities and provides quantification of the uncertainties in the resistivity model. We apply the inversion methodology to synthetic geothermal test cases where three prior models for the geothermal reservoir were used: one small in size, but with the correct center location; another with correct size, but wrong location; and a third with small size and wrong location. The test cases showed that the clay cap was accurately estimated and the reservoir was well approximated, both in terms of shape and location.
Presentation Date: Thursday, October 18, 2018
Start Time: 8:30:00 AM
Location: 213A (Anaheim Convention Center)
Presentation Type: Oral
The problem of discriminating between effects of saturation and pressure changes on geophysical data when monitoring CO2 sequestration is considered. We propose an inversion methodology where controlled-source electromagnetic (CSEM) inversion for approximate location of regions of saturation changes is performed and subsequently used as prior information in a Bayesian inversion of seismic waveform data (in the acoustic approximation) for identification of regions of both saturation and pressure changes. To facilitate identification of regions we utilize a level-set type representation of the unknown properties. Both the CSEM and seismic inversions are performed using the ensemble Kalman filter, which updates property models without calculating sensitivities, and provides the ability to quantify uncertainty in the models. The proposed inversion methodology is applied to synthetic CO2-monitoring test cases. It was found that it was necessary to use information on saturation changes from inversion results from CSEM as prior information in the seismic inversion to be able to accurately locate both saturation and pressure changes.
Presentation Date: Tuesday, October 18, 2016
Start Time: 8:25:00 AM
Presentation Type: ORAL
The upstream mobility scheme is widely used to solve hyperbolic conservation equations numerically. When heterogeneities in the porous medium are introduced, the flux function in these equations attains a spatial discontinuity. In many systems the
upstream mobility scheme approximates a solution close to the solution produced by solving the associated Riemann problem, but in the case of a heterogeneous system there exists no convergence analysis.
In this work the upstream mobility scheme is applied to a counter-current flow in a reservoir where discontinuities in the flux function are introduced through the permeability. Examples of such counter-current flow systems in heterogeneous reservoirs are
Water-Alternating-Gas (WAG), Steam-Assisted Gravity Drainage (SAGD) and flow of CO2 and brine. The flux functions in these systems involve both advection and gravity segregation components. In this work we show that the upstream mobility scheme may exhibit large errors compared to the physically relevant solution for some combinations of flux functions in such a system. We show that a small perturbation of the relative permeability values can lead to a large difference in the solution produced by
the upstream mobility scheme.
We look at the one-dimensional case since the Riemann solutions are mostly unknown for more than one dimension. However, in the multidimensional case, many numerical methods use one-dimensional calculations for the flux in the direction normal
to the boundaries of the discretization cell. Not only does the scheme encounter large errors compared to the physically relevant solution, but the solution also lacks entropy consistency. Studies of these errors and the convergence performance of the scheme are important due to the extensive use of the upstream mobility scheme in the reservoir simulation community.