During the last year, the Celia Group continued to develop its large-scale modeling framework with a focus on leakage estimation. This included a number of new components to the models, a great improvement in model robustness, development and initial application of a hybrid analytical-numerical model, and development of an initial beta-version of a web interface for the group’s models.


Figure 10. Location of Wabamun Lake study area in Alberta, Canada (a) and existing wells (b).

Semi-analytical Model for Leakage Estimation

Our semi-analytical model is designed to model injection of CO2 into a deep saline aquifer, in a domain that includes multiple layers and multiple (possibly leaky) passive wells. As described in the past, this model uses a set of analytical solutions, driven by standard two-phase flow equations, to solve for the location and evolution of the CO2 injection plume, all secondary plumes caused by leakage of CO2 along well segments, the flow of brine both within the formations and along the leaky wells, and the pressure field at all points within the domain. During the last year, the software was completely re-written so that the code is now much more robust and is about ten times more efficient. Some of the relevant mathematics that underlies the algorithms can be found in a recent paper that has just appeared (online) in the journal Environmental Science and Technology.

The researchers continue to apply the code to a specific site in Alberta, Canada (Figure 10), where they have worked with colleague Stefan Bachu to put together a data set. Because the group can run tens of thousands of simulations, they can perform a range of probabilistic risk assessment calculations. The latest publication related to this work is a GHGT-9 paper where risk of leakage as a function of depth of injection is examined. Figure 11 is taken from that paper, and shows example leakage results for injections into different layers. The layers and some of their properties are shown in Table 1. Three important points related to the results are highlighted here. First, there is an obvious difference in the number of wells that penetrate the caprock of a formation, as a function of depth. While those numbers might be expected to map directly to leakage amounts, this is not seen in Figure 11, especially when analyzing the Nordegg and Nisku formations. This is because this is only a single injection plume, and the characteristics of the formations make those plumes quite different. This highlights the second important point which is related to formation injectivity.

Table 1: Data for layered domain. Shaded rows correspond to injection formations.

While the Nordegg formation has more than an order of magnitude more wells penetrating its caprock, as compared to the Nisku, the number of wells contacted after 50 years by a single injection plume is actually less (13 versus 31), and the leakage associated with injection into the Nisku is slightly higher. All of this is driven by limits on injection rates due to an imposed limit that the maximum injection pressure should not exceed 90% of the estimated fracture pressure. This highlights the importance of fracture pressures limiting injection rates and the need for careful strategies to design injection wells. The third point to highlight is the two different estimates for leakage probabilities in Figure 11, each based on a different assumed structure of the input probability distribution for the leaky wells. One uses a standard bi-modal lognormal distribution, while the second attempts to incorporate ‘soft’ information about the wells based on a scoring system proposed by Watson and Bachu, which was mapped into a permeability field. This highlights the continued importance of parameter identification and the critical part that the BP field program plays in quantifying leakage risk.

Figure 11. Leakage results for CO2 injection into different layers underlying the study area.

Numerical Sharp-Interface Model and Hybrid Model

The semi-analytical model used above requires a number of simplifying assumptions, some of which may be inappropriate for a given system. For cases where the simplifications cannot be justified, the team has developed a numerical implementation that maintains the basic assumptions of a macroscopic sharp interface and vertical equilibrium, but eliminates the need for more severe assumptions like homogeneous and horizontal formations. They have now implemented an initial version of this model and tested it in a variety of ways, including an international code comparison.

One of the test problems involved in the code comparison was a faulted part of the Johannsen formation, off the Norwegian coast. Predictions of plume extent and migration using a relatively simple sharp-interface model compared well with full industry simulators like Eclipse – see Gasda et al., 2009 and Class et al., 2009. Note that this test problem did not include any leakage, so it was a straight-forward injection into a single formation, with the complexity being associated with the geometry of the formation and geological heterogeneity.

A second test problem included leakage along a single existing well in a relatively simple three-layer domain, with two permeable formations separated by an impermeable caprock, as depicted in Figure 12. This problem was motivated by earlier published work in which a similar problem was solved. This test problem was solved using both a semi-analytical approach and a numerical approach. For the numerical solution, the domain was discretized using coarse grid blocks, and represented the leaky well using a sub-scale analytical solution borrowed in part from the semianalytical solutions.

Figure 12. Schematic of test problem from Class et al. (2009).
Figure 13. Different code results for test problem [From Class et al., 2009].

This combination of coarse-scale numerical approximation, which captures geometric and parameter heterogeneities, and fine-scale analytical solutions that capture the local leakage behavior, is referred to as a hybrid numerical-analytical solution. This hybrid solution worked very well in the comparison exercise, and is now their preferred method to solve problems with relatively complex geology that also include potentially leaky wells or other concentrated leakage pathways. The test problem set-up is shown in Figure 12, and the set of solutions, including both the group’s semi-analytical (Elsa) and hybrid (VESA) solutions, is shown in Figure 13. Many other details can be found in the manuscripts of Gasda et al. (2009) and Class et al. (2009), which are currently under review for publication in the journal Computational Geosciences.

The researchers are now in the process of putting together a broad modeling framework that can incorporate both numerical and analytical solutions into an overall simulation. They refer to this as a ‘hierarchical modeling framework’ in that users will be given options that range from simple to relatively complex simulation tools, and they hope to report favorably on this new modeling paradigm in future reports.

Other Uses of Storage Group Models

In addition to the applications described above, several others have used these models over the last year. Jason Deardorff, a graduate student at the Colorado School of Mines, completed an MS Thesis titled The Geologic Carbon Sequestration Potential of the Denver-Julesburg Basin of Colorado: Applied Methodologies for Basin Scale and Site-specific Assessment of CO2 Sequestration Potential. Jason used the group’s analytical models to estimate storage potentials for a number of formations in the Colorado area and is now employed by the U.S. Environmental Protection Agency. Professor Mark Person from Indiana University was inspired by the sharp interface approach, specifically the paper of Nordbotten and Celia (2006), and used the group’s approach to model a number of injection scenarios in the Mt Simon formation in Illinois. Some of that work was presented in December 2008 at the American Geophysical Union meeting (Person et al., 2008).