(544c) Estimation of Permeability and Porosity for CO2 Sequestration in Heterogeneous Formations with Derivative-Free Optimization Based On Observed Data

The modeling and simulation of CO2 sequestration in geological formations have received increased attention in recent years.  Oftentimes, some of the parameters such as porosity and permeability in these models remain uncertain, as it is unrealistic to fully characterize the heterogeneity of geological formations.  Therefore, to quantify the impact of such uncertainties on CO2 plume migration in heterogeneous formations, parameters such as porosity and permeability must be estimated from observed data.  The methodologies of this kind of uncertainty quantification problem have been comparatively studied in oil production forecasts[1].  However, the optimization algorithms used for inverse modeling are mostly based on gradient methods which require the gradient of objective function.  In numerical simulations of CO2 sequestration, to obtain such gradient information is computational prohibitive.  To cope with the high computational requirements, we apply various derivative-free optimization (DFO) methods [2] to solve this inverse problem.

In our work, a 3D benchmark for CO2 injection into a synthetic heterogeneous (known porosity and permeability field) saline aquifer is modeled using TOUGH2 [3].  Selected model outputs, such as gas saturation map, from TOUGH2 simulations are perturbed with random Gaussian noise to generate a test data set.  The data set is then used to test the ability of 28 DFO solvers to infer the original porosity and permeability field using Bayesian inference.  The inferred porosity and permeability field are then used for uncertainty quantification of CO2 plume migration.  Extensive computational results are reported to evaluate the ability of the 28 algorithms to estimate unknown porosities and permeabilities correctly from the observed data.

References cited:

1. Floris, F. J. T., Bush, M. D., Cuypers, M., Roggero, F. and Syversveen, A-R., Methods for quantifying the uncertainty of production forecasts: a comparative study, Petroleum Geoscience, 2001(7), S87-S96

2. Rios, L. M. and Sahinidis, N. V., Derivative-free optimization: A review of algorithms and comparison of software implementations, http://thales.cheme.cmu.edu/dfo.

3. Pruess, K. ECO2N: A TOUGH2 fluid property module for mixtures of water, NaCl, and CO2. Lawrence Berkeley National Laboratory: Berkeley, 2005.