Grantee Research Project Results

Final Report: A Hierarchical Modeling Framework for Geological Storage of Carbon Dioxide

Objective:

The project had four general goals and objectives: (1) to develop and enhance a set of analytical and numerical computational tools for simulation of CO₂ injection, migration, and possible leakage; (2) to develop a "hierarchical modeling framework" within which different computational tools can be combined to produce effective hybrid models; (3) to provide guidance on level of model complexity for different scenarios; and (4) to provide simple-to-use web-based interfaces for different versions of the codes we develop.

Summary/Accomplishments (Outputs/Outcomes):

• We have developed a set of fairly general numerical models based on vertically integrated governing equations under the assumption of vertical equilibrium (VE). These models provide significant computational advantages because of the reduction of dimensionality (three dimensions (x,y,z) reduced to two dimensions (x,y)). We note that these models do not require an assumption of a macroscopic sharp interface separating the two fluids (CO₂ and brine) – a capillary transition zone in the vertical direction, consistent with the local-scale capillary pressure-saturation relationship, fits naturally into these models. See Gasda et al. (2012) or Nordbotten and Celia (2012) for details. Our numerical models include all major processes relevant to the CO₂ storage problem, and can accommodate arbitrary heterogeneities in the horizontal directions. Processes modeled include different kinds of leakage through the caprock, including concentrated leakage along old wells or faults, and diffuse leakage through caprock formations, all in the context of multiple aquifer and aquitard sequences. The diffuse leakage treatment can be found in Janzen (2010) and Bandilla et al. (2013), while the treatment of leakage along old wells and along faults can be found in Celia et al. (2011) and Kang et al. (2014). Our numerical models also include capillary trapping of the injected CO₂ (see Gasda et al., 2012) and more recently, we have derived a more general treatment of hysteresis and shown how local-scale hysteresis in both capillary pressure and relative permeability can be incorporated into vertically integrated models (Doster et al., 2013, 2014). These models also include dissolution of CO₂ into brine with subsequent convective mixing (Gasda et al., 2011). In the dissolution work, we use an upscaled representation of the convective mixing based on averaging of highly-resolved fine-scale simulations of the unstable mixing in the vertical; the results are reasonable given the overall scales involved in the problem. These large-scale numerical models have been applied to several realistic scenarios, including simulations of the Illinois Basin (Bandilla et al., 2012), the Basal Formation in the Alberta Basin (and adjacent basins) (Huang et al., 2014), and the Johanson formation under the North Sea (Gasda et al., 2012). As mentioned earlier, all of these models allow for a general capillary transition zone, thereby alleviating the assumption of a sharp interface separating the CO₂ and brine. The models that include dissolution use an upscaled expression for convective mixing, based on detailed simulations at the fine scale. These models capture the essential behavior of the dissolution process while allowing us to maintain computational efficiencies.
• We have enhanced and applied our analytical and semi-analytical models for CO₂ injection and migration; these models also include leakage of both CO₂ and brine along old wells. These analytical models require additional simplifying assumptions, including horizontal and homogeneous aquifers, but they provide very efficient simulations, orders of magnitude faster than analogous numerical models. This efficiency allows injection into systems with many geological layers (alternating aquifers and aquitards) and many potentially leaky wells to be simulated in a few minutes on a single-processor computer. The paper of Celia et al. (2011) shows a specific example of how large-scale injection into realistic formations that have many potentially leaky wells, and many geological layers in the vertical direction, can be simulated. A sedimentary sequence in the Alberta Basin was used to study potential leakage of both CO₂ and brine along a set of old wells. Results indicate that leakage rates are likely to be relatively low, for both CO₂ and brine. The study of Nogues et al. (2012) expanded the studies of Celia et al. (2011) to identify specific measures of well properties that would lead to acceptably low leakage rates. In that study, we developed practical guidance for how well leakage might be analyzed when specific maximum leakage targets are identified (for example, no more than 0.1% leakage after 50 years of injection). The results in that paper showed what kinds of statistics the effective permeability along old wells must satisfy in order to meet target leakage criteria. We note that the guidance provided in Nogues et al. can be coupled with the implied values for well permeabilities derived in Tao and Bryant (2014) to indicate an expected low probability of leakage along old wells. In addition, we have derived a new analytical solution to represent fluid behavior in the vicinity of a leaky fault (Kang et al., 2014). That work shows how the fault properties play an important role in the solution, and how in the vicinity of the fault vertical flow effects, which are included in the local-scale analytical solution, can be important for proper calculation of the leakage rates.
• We expanded the use of our simplified computational models to study new paradigms in CO₂ storage. We published two paper (Bandilla et al., 2012a,b) in which we examined the large-scale impacts of basin-wide injections into the Mt. Simon aquifer. The extensive overlap of the Areas of Review led to exploration of brine production as a method of pressure control. In Court et al. (2012c), we studied more carefully the idea of using brine extraction for the purpose of pressure control. This subsequently led us to consider the idea of CCS more broadly, consistent with the expanded idea of CCUS (carbon capture, utilization, and storage). In particular, we began to explore potential synergies between geothermal energy production and CO₂ injection. The papers of Elliot et al. (2013) and Buscheck et al. (2012) examined a number of different aspects of this idea, where heat from the produced fluids was extracted for geothermal energy. The brine extraction provides the corollary benefit of pressure control as well as control of the CO₂ plume extent, while the CO₂ injection provides complementary pressure support for the geothermal production.
• We have recently developed a new class of models that relaxes the vertical equilibrium (VE) assumption while still using a vertically integrated framework. This gives the computational advantages of reduced spatial dimensionality while allowing for dynamics of CO₂ and brine flows in the vertical direction. This is as opposed to the assumption of vertical equilibrium where the CO₂ is always above the brine (instantaneously) with the two segregated fluids in pressure equilibrium. The underlying ideas are presented in the recent paper of Guo et al. (2014). This concept follows from the idea that VE models can be understood in the broad context of multi-scale models – this is explained in the textbook of Nordbotten and Celia (2012). This new model, which includes vertical dynamics, provides a model of intermediate complexity, where much of the dynamics inherent in fully three-dimensional models can be captured while still maintaining significant computational reductions. We are in the process of studying the numerical properties of this approximation and identifying its limitations, in particular the ways in which both pressure and saturation need to be treated when we include heterogeneity in the vertical direction.
• In terms of the idea of “hierarchical” models, we have achieved this objective through the broader framework of multi-scale modeling. The general idea of the multi-scale framework is presented in Nordbotten and Celia (2012), where vertically integrated models were analyzed by identifying the vertical dimension as the “fine scale” and the horizontal dimensions as the “coarse scale”. This framework provides significant insights into vertically integrated models, and led directly to the derivation of the new ‘dynamic’ model of Guo et al. (2014). In addition to this broad framework for vertically integrated models, we have also provided additional fine-scale representations where analytical solutions at the fine scale (now in the horizontal direction) are embedded into numerical solutions at the coarse scale. The overall idea is to use local-scale analytical or semi-analytical solutions to represent local features like leaky wells or leaky faults, in the context of large-scale numerical models. The use of these local analytical solutions, which define a fine scale in the (x,y) horizontal plane, avoids the need for fine numerical discretization around these local features. These kinds of local-scale corrections have been developed for both pressure and CO₂ saturation profiles in the vicinity of an injection well (Janzen, 2010) and in the context of leakage into a fault (Kang et al., 2014). Both of these follow, broadly, from the earlier work of Nordbotten and Celia (2006a,b) on analytical solutions and on two-phase upconing around leaky wells. The recent work on faults, which was much more complicated than anticipated, requires inclusion of information about both the formation and the fault region – see the details in Kang et al. (2014). We believe that these analytical solutions, which are embedded into larger-scale numerical grid blocks in the (x,y) plane, provide a very flexible framework for enhanced multi-scale modeling for practical CO₂ injection problems.

Conclusions:

References:

1. Nordbotten, J.M. and M.A. Celia, "Similarity Solutions for Fluid Injection into Confined Aquifers", Journal of Fluid Mechanics, 561, 307-327, 2006a.
2. Nordbotten, J.M. and M.A. Celia, "An Improved Analytical Solution for Interface Upconing Around a Well", Water Resources Research, 42, W08433 (doi:10.1029/2005WR004738), 2006b.
3. Nordbotten, J.M. and M.A. Celia, Geological Storage of CO2: Modeling Approaches for Large-scale Simulation, John Wiley and Sons, Hoboken, NJ, 235 pages, 2012.
4. Tao, Q. and S.L. Bryant, “Well Permeability Estimation and CO2 Leakage Rates”, International Journal of Greenhouse Gas Control, 22, 77-87, 2014.

Supplemental Keywords:

Progress and Final Reports: