Developing and Validating Simplified Predictive Models for CO2 Geologic Sequestration

Abstract

CO₂ sequestration in deep saline formations is increasingly being considered as a viable strategy for the mitigation of greenhouse gas emissions from anthropogenic sources. In this context, full-physics compositional simulations are routinely used to understand key processes and parameters affecting pressure propagation and buoyant plume migration. As these models are data and computation intensive, the development of computationally-efficient alternatives to conventional numerical simulators has become an active area of research. Such simplified models can be valuable assets during preliminary CO₂ injection project screening, serve as a key element of probabilistic system assessment modeling tools, and assist regulators in quickly evaluating geological storage projects. We present three strategies for the development and validation of simplified modeling approaches for CO₂sequestration in deep saline formations: (1) simplified physics-based modeling, (2) statistical-learning based modeling, and (3) reduced-order method based modeling.

In the first category, a set of well-designed full-physics compositional simulations is used to develop correlations for dimensionless injectivity as a function of the slope of the CO₂ fractional-flow curve, variance of layer permeability values, and the nature of vertical permeability arrangement. The same variables, along with a modified gravity number, can be used to develop a correlation for the total storage efficiency within the CO₂ plume footprint. Furthermore, the dimensionless average pressure buildup after the onset of boundary effects can be correlated to dimensionless time, CO₂ plume footprint, and storativity contrast between the reservoir and caprock.

In the second category, statistical “proxy models” are developed using the simulation domain described previously with two different approaches: (a) classical Box-Behnken experimental design with a quadratic response surface, and (b) maximin Latin Hypercube sampling (LHS) based design with a multidimensional kriging metamodel fit. For roughly the same number of simulations, the LHS-based metamodel yields a more robust predictive model, as verified by a k-fold cross-validation approach (which requires splitting the data into training and test sets) as well by validation with an independent dataset.

In the third category, a reduced-order modeling procedure is utilized that combines proper orthogonal decomposition (POD) for reducing problem dimensionality with trajectory-piecewise linearization (TPWL) in order to represent system response at new control settings from a limited number of training runs. Significant savings in computational time are observed with reasonable accuracy from the POD-TPWL reduced-order model for both vertical and horizontal well problems – which could be important in the context of history matching, uncertainty quantification and optimization problems.

The main contribution of this paper is the development and validation of simplified modeling approaches that will enable rapid feasibility and risk assessment for CO₂sequestration in deep saline formations.