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The four major trapping mechanisms that facilitate storage of CO2 in subsurface aquifers include structural trapping, in which more-buoyant CO2 accumulates against the essentially impermeable cap rock; dissolution trapping, in which CO2 dissolves in the in-situ brine; residual trapping, where CO2 exists as a residual phase of sufficiently low saturation that it does not flow; and mineral trapping, where CO2 reacts chemically to form a solid phase (Benson et al., 2005). These trapping mechanisms are depicted in Figure 1.2, where the proportion of total trapping with time is illustrated.

This figure should be viewed qualitatively, since the details of storage operations will be site specific. Structural trapping, which dominates at early times, is often considered to be the least secure trapping mechanism because structurally trapped CO2 can escape if there are fractures in the cap rock. Such fractures may be previously


Figure 1.2: Trapping mechanisms for aquifer carbon storage (from Benson et al.,2005)

existing but undetected, or they may be generated during CO2 injection.

It is evident in Figure 1.2 that mineral trapping does not become important until long time frames (thousands of years). Farshidi et al. (2013) found that for a typical sandstone aquifer system, mineralization would account for around 0.5% of trapping after 100 years and around 5% after 2000 years. Since coupled reactive-transport modeling is computationally demanding and mineral trapping only represents a small portion of total trapping over relevant time frames, mineral trapping can often be ignored in modeling studies. In some geological settings however, mineral trapping will be important and must be included in simulations. For more discussion of the impact of mineralization see, e.g., Pruess et al. (2003) and Fan et al. (2012).

Residual trapping is an important trapping mechanism that should not be ignored in modeling studies. The immobilization of CO2 via residual trapping is often explained using a pore doublet or snap-off model (Adler & Brenner, 1988). In both cases, surface tension differences between fluids cause small pockets of CO2 to become

1.1. LITERATURE REVIEW disconnected from the main plume. Residual trapping is modeled in simulators by including hysteresis in the relative permeability curves; i.e., through use of different imbibition and drainage curves for CO2 relative permeability. In one study with a particularly high degree of hysteresis, it was shown that residual trapping can store 60% of the injected CO2 (Doughty, 2007). Similar studies by Juanes et al. (2006) and Flett et al. (2004) confirm the importance of hysteresis in carbon storage modeling.

Several groups (e.g., Bennion & Bachu, 2006; Krevor et al., 2012) have measured relative permeability curves for CO2 and brine from core-flooding experiments on various rock samples. In particular, Krevor et al. (2012) measured both drainage and imbibition curves for a variety of aquifer sandstones. They presented a method to extrapolate experimental curves to the high CO2 saturations that may occur in the aquifer but are difficult to achieve experimentally.

Several studies have reported comparisons of simulations with field performance.

In particular, vertical seismic profiling, cross-well seismic and observation well data from the Frio Experiment (Hovorka et al., 2006; Doughty et al., 2008; Daley et al., 2008; Xu et al., 2010) have been used to confirm model predictions regarding plume distribution and migration. Doughty et al. (2008) also performed manual history matching to improve the Frio site characterization. Similarly, a recent study by Singh et al. (2010) was conducted to calibrate simulation model parameters to seismic data from the Sleipner project in the North Sea. With minor adjustments to the relative permeability curves, a reasonable match for the location and size of the CO2 plume was obtained. These studies suggest that existing computational tools can be applied to model carbon storage in saline aquifers, provided sufficient data are available.

The effect of grid resolution in CO2 storage modeling has been considered by Yamamoto & Doughty (2011). They found that coarse-grid models overestimate residual and dissolution trapping and underestimate the extent of plume movement.

This motivates the need for grid refinement analysis in numerical studies of CCS. As noted above, computationally efficient (e.g., coarse-grid) models are, however, ideal for optimization and data assimilation procedures.

Previous researchers have proposed different strategies for reducing the risks associated with carbon storage. For example, Leonenko & Keith (2008) showed that CO2 dissolution could be accelerated by producing brine away from the injection site


and reinjecting this brine into regions occupied by CO2. This facilitated additional mixing of CO2 with brine to increase dissolution. Anchliya et al. (2012) extended this idea and engineered an injection strategy that was able to eliminate structural trapping entirely, while also limiting pressure buildup. Their proposed injection scenario entails several horizontal brine producer and injector wells located around each CO2 injection well, as shown in Figure 1.3. Because it involves additional wells and brine injection and production, this approach would add substantial cost to the storage operation. Similar models, with a brine injector located above a CO2 injector, have been analyzed by Nghiem et al. (2009, 2010). In those studies, several injection scenarios were evaluated with respect to multiple objective functions. For each injection scenario, total residual trapping and total dissolution trapping was measured to create a Pareto (bi-objective) front. The latter study also considered a third objective function (the volume of injected brine) to create a three-dimensional Pareto front.

The impact of different CO2 injection and brine production strategies on pressure was also investigated by Bergmo et al. (2011) using models of the Utsira formation at Sleipner. They compared cases with and without brine producers and considered different numbers of CO2 injectors. For the cases considered, they found that local pressures beneath the cap rock were more affected by the number of CO2 injectors than by the existence of brine producer wells. In one example with a single CO2 injector, the maximum pressure increase beneath the cap rock was 44 bar. This was reduced to 30 bar when three CO2 injectors were used to inject the same volume and further reduced to 23 bar when brine production wells were added.

1.1.2 Optimization of CO2 storage operations

As shown in Figure 1.1, the optimization of CO2 storage operations involves a number of steps, both a-priori (that is, before injection data and any monitoring data are available) and within the closed loop. A-priori optimization involves the determination of optimal well placements for both CO2 injectors and monitoring wells (sensors). Closed-loop optimization involves updating the geologic model using injection and monitoring data (also known as history matching) and re-optimizing well control settings based on the updated model.

1.1. LITERATURE REVIEW Figure 1.3: Engineered injection method to promote dissolution and residual trapping (adapted from Anchliya et al., 2012) Well placement optimization is often viewed as an a-priori process, because injection wells are drilled before a significant amount of dynamic data are available. In reality, wells would be drilled in sequence or additional wells may be drilled after CO2 injection has started, so some data may be available (though this is not considered in our work). Well rate-control optimization is also performed a-priori because the optimal well locations will depend on how the wells are to be controlled. Rates can, however, also be optimized during the closed-loop process.

We will first discuss literature pertaining to well placement optimization, then well control optimization, and then the joint (simultaneous) optimization of both placement and control. A brief discussion of how previous researchers have dealt with geologic uncertainty is also provided. Finally, we will discuss literature related to data assimilation and the related a-priori problem of determining optimal sensor placements.


Well placement optimization

Well placement optimization in heterogeneous geologic formations is a complicated problem because the objective function surface can be highly discontinuous with multiple local optima. While there has not been much, if any, research reported on optimizing well placements for CO2 storage, there is a wealth of research that has been conducted to solve the analogous problem in oil field applications, for which a variety of techniques have been considered. Most studies applied stochastic and/or derivative-free optimization techniques because these methods tend to avoid becoming trapped in local optima. Gradient based methods such as Simultaneous Perturbation Stochastic Approximation (e.g., Bangerth et al., 2006), adjoint based methods (e.g., Sarma & Chen, 2008; Zandvliet et al., 2008), and ensemble based methods (e.g., Leeuwenburgh et al., 2010) have also been applied with some success.

Derivative-free stochastic search methods such as Genetic Algorithms (GA), Simulated Annealing (SA), and Particle Swarm Optimization (PSO) have been widely applied to solve well placement optimization problems for oil field applications. These methods are straightforward to implement, parallelize naturally, and are robust with respect to rough optimization function surfaces. Guyaguler & Horne (2000) and Yeten et al. (2003) applied GA for well placement optimization of vertical and nonconventional wells respectively. Onwunalu & Durlofsky (2010) compared the performance of PSO and GA in determining optimal well placement and type for both vertical wells and nonconventional wells. In that work, PSO was found to outperform GA for the problems considered. See Isebor (2013) for a comprehensive review of derivative-free optimization techniques for oil field operations.

Hybrid algorithms have also been developed to provide both global search and local convergence properties. Guyaguler & Horne (2000) combined GA with a polytope algorithm to determine optimal placements of standard vertical wells. Similarly, Yeten et al. (2003) applied a method that combines GA with a local hill climber algorithm to optimize the type and location of nonconventional wells. In both of these studies, the hybrid algorithm was found to outperform the individual methods.


Well control optimization

Well control optimization involves determining optimal time-dependent operating variables (e.g., rates and/or bottomhole pressures) in order to optimize an objective (e.g., minimize leakage risk or maximize net present value). It can be performed both a-priori and during closed-loop operations, as shown in Figure 1.1. The optimization surface for the well control problem is generally more continuous than for the well placement problem, which enables gradient methods to be used successfully.

Previous researchers have applied both gradient-based and derivative-free techniques to solve this problem in the context of oil field operations.

Of particular interest are studies that performed well control optimization within a closed-loop setting. In this context, both Sarma et al. (2006) and Jansen et al.

(2005) used gradient-based methods with gradients calculated using adjoint procedures. See Jansen (2011) for a detailed review of adjoint procedures for use in oil field optimization. While adjoint methods display fast convergence and require very few simulation runs, gradients must be provided by the simulator, which is not always practical. Echeverr´ Ciaurri et al. (2011) compared derivative-free methods such as ıa Hooke-Jeeves Direct Search – HJDS (Hooke & Jeeves, 1961) and Generalized Pattern Search – GPS (Kolda et al., 2003) against several gradient methods. They found both HJDS and GPS to be effective approaches in well control optimization problems.

In the context of carbon storage operations there has been only limited study of well control optimization. Kumar (2007) determined optimal time-varying injection rates for wells in a two-dimensional heterogeneous model to minimize the fraction of structurally trapped CO2. A conjugate gradient method was applied in that work.

Recently, Shamshiri & Jafarpour (2012) used a quasi-Newton, gradient-based approach to determine the optimal time-dependent injection rates for multiple CO2 injectors in a three-dimensional model. In that case, optimality referred to either maximizing residual and dissolution trapping or maximizing the ‘sweep efficiency’ of the CO2 plume. They also accounted for geological uncertainty, in one example, by optimizing over multiple realizations. In neither of these studies, however, was the optimal placement of the injectors considered.


Joint optimization of placement and control

As mentioned previously, optimal well placements will depend on how the wells are to be operated, and visa-versa. Thus, the a-priori optimization problem should consider well placement and control as a joint optimization, rather than optimize placements and controls sequentially. Some investigators have studied the joint optimization problem for oil field applications. Recent publications include Bellout et al. (2012), who used pattern search methods combined with an adjoint procedure, and Li & Jafarpour (2012), who used a simultaneous perturbation and stochastic approximation method in conjunction with an adjoint technique. In both cases the adjoint procedure was used for the optimization of well settings (not for optimizing well locations).

These studies demonstrated the advantage of the simultaneous optimization of well placement and control over a sequential approach.

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