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Of particular relevance is the work of Isebor et al. (2013), who developed a technique combining a global stochastic search algorithm (PSO) hybridized with a local pattern search algorithm (Mesh Adaptive Direct Search – MADS). The method, called PSO-MADS, was also able to optimize the number and type of well (e.g., injector or producer) and handle general constraints using a filter method. This approach was shown to be robust and effective for the joint optimization problem.

Optimization under geologic uncertainty

Geologic uncertainty is often accounted for by optimizing the expected value or some other statistical metric of the objective function over several geologic realizations (see, for example, Guyaguler & Horne, 2004; Shamshiri & Jafarpour, 2012). In general, selecting more realizations leads to more reliable results, but also increases computational costs. Previous researchers have achieved reductions in computational time by clustering realizations using statistical proxies and applying specialized selection strategies (Artus et al., 2006). Another approach, proposed by Wang et al. (2012), is to include geologic uncertainty using a ‘retrospective optimization’ framework. In this method, an increasing number of geologic models are used as the optimization proceeds toward convergence.


Data assimilation and optimal sensor placement

Data assimilation (also known as history matching or model updating) refers to the determination of one or more geological models that match observed dynamic data to within some tolerance. Several studies have focused on history matching in the context of carbon storage. Some of these used data collected from actual storage operations, while others used synthetic data to test methodologies. Many of the history matching studies to date (e.g., Doughty et al., 2008; Ennis-King et al., 2011) considered simplified facies models and included only a small number of geological parameters in the history matching process. In the case of Doughty et al. (2008), cross-well seismic and vertical seismic profile (VSP) data were collected (Daley et al.,

2008) from the Frio formation near Houston, Texas. The forward model for history matching involved both flow and seismic modeling, with seismic signals providing the data that were matched. In the case of Ennis-King et al. (2011), bottomhole pressure data from the depleted Naylor gas field in Southeastern Australia were used for history matching.

Parameterization procedures can be applied to reduce the dimension of the set of geological variables that must be determined while enabling candidate solutions to implicitly honor a prior geological model. One such technique, the KarhunenLo`ve (K-L) expansion, has been used for performing data assimilation in oil field e applications by, e.g., Oliver (1996), Reynolds et al. (1996) and Sarma et al. (2006).

K-L expansion is synonymous with principal component analysis (PCA). As such, it is applicable to problems where the geologic model is multi-Gaussian, that is, based on two-point spatial geostatistics. For non-Gaussian models (i.e., characterized by multipoint spatial geostatistics), kernel principal component analysis (KPCA) may be used instead (Sarma et al., 2008).

Ensemble Kalman filter techniques have become popular in petroleum engineering and related subsurface management problems, in part because these methods are noninvasive with respect to the simulator. See Oliver & Chen (2011) for a recent review of Kalman filter techniques for data assimilation. A comprehensive overview of history matching for oil field applications can be found in Oliver et al. (2008).

The optimal placement of sensors in carbon storage aquifers has also been addressed. JafarGandomi & Curtis (2012) used a Bayesian optimal experimental design


method to guide the placement of cross-well seismic sensors along a wellbore. Magnant (2011) investigated the same problem from an information theory standpoint.

In both of these studies, sensors were placed to maximize some measure of entropy or data ‘information,’ rather than a problem-specific goal. The optimal placement of pressure sensor wells for CO2 storage operations has not yet been addressed within an optimal experimental design framework.

1.1.3 Leak detection Much research has been dedicated to understanding the physical processes of CO2 leakage through conduits such as fractures and abandoned wells. Jordan et al. (2011) used a fault density distribution model to estimate the probability of a plume encountering a fault. For their case study in the San Joaquin Basin, they found that a previously planned injection site had a 3% chance of encountering a significant fault.

See Lewicki et al. (2007) for more information and examples of flow through faults in CCS related operations. Leakage through abandoned wells has also been studied.

Nordbotten et al. (2005) developed a semi-analytical model for flow through leaky wellbores. The likelihood of encountering leakage through an abandoned well was investigated by Gasda et al. (2004).

Many studies have discussed monitoring options for carbon storage operations.

Methods relying on surface detection of CO2 have been proposed by, e.g., Lewicki et al. (2005) and Fessenden et al. (2010). While these methods may be effective at determining when leakage has occurred, leakage should ideally be identified before it has reached the surface, to enable remediation strategies to be applied as early as possible.

At the In Salah and Sleipner storage projects, various types of monitoring data have been used for the early detection of leakage. This includes well data, seismic data, surface gas monitoring, tracers, and satellite interferometry. At the In Salah site, a combination of surface uplift data and measured CO2 breakthrough at a monitoring well confirmed that leakage had occurred. This leakage was largely attributed to one of the three CO2 injectors (Ringrose et al., 2009), which was subsequently shut in.

Because pressure responses in the subsurface propagate quickly, pressure data from monitoring and injection wells in the storage formation and/or overlying aquifer

1.2. SCOPE OF WORK may be useful in the early detection of leaks. Javandel et al. (1988) proposed a method to determine the location and transmissibilty of an abandoned well using pressure data collected over 50 days from nearby injection and monitoring wells.

Their method assumes that the aquifer pressure can be characterized using the Theis equation (Theis, 1935), which is an analytical approximation of the pressure response from single-phase injection into an infinitely large, two-dimensional, homogeneous aquifer. While this method ignores geologic uncertainty and uses an oversimplified aquifer model, it shows that leakage detection from pressure data may be possible.

The detectability of leaks through abandoned wells and fractures using pressuretransient data from wells in the overlying aquifer was analyzed by Chabora & Benson (2009). They found that this data can indicate CO2 breakthrough in some cases, though their tests were performed on simplified aquifer models with known geology. Sun & Nicot (2012) confirmed that pressure anomalies indicating leakage are detectable even when measurement error and spatial heterogeneity are considered.

More recently, Sun et al. (2013) used a probabilistic collocation method to determine when pressure data might be used to detect leakage. The method considers the signal-to-noise ratio of pressure anomaly data compared to background noise. This approach provides an effective means for detecting when a leak exists. The inverse problem of determining the size and position of leaks was not addressed. Furthermore, the detectability of multiple leaks using pressure data remains to be investigated.

1.2 Scope of work The purpose of this work is to develop new methodologies to manage the risk of leakage in CCS operations. We now describe the specific topics addressed in this thesis.

• We develop and apply computational optimization techniques, which are in many ways analogous to those developed for oil field applications, to facilitate safe modes of storage and/or minimize the risk of leakage in carbon storage operations. In particular, we extend the work of Shamshiri & Jafarpour (2012), Nghiem et al. (2010) and Kumar (2007) in that we simultaneously optimize both CO2 injection well placement and time-varying injection rates for each


well. A Hooke-Jeeves Direct Search algorithm is used for the optimizations.

Our examples involve multiple horizontal wells placed in heterogeneous threedimensional aquifer models with aquifer geology assumed to be known. We also optimize injection control parameters governing a process referred to as ‘brine cycling.’ The optimal trade-off between brine cycling cost and the level of risk reduction is presented as a Pareto front.

• We present a set of procedures applicable for a-priori optimization and closedloop operation of CCS processes. In this case aquifer geology is considered to be uncertain and defined by a prior model. Some of the computational procedures are again related to techniques previously applied for oil fields, but several of our treatments are new. We determine the optimal well locations, and initial estimates for optimal time-varying CO2 injection rates, under geological uncertainty. These optimizations are performed using Particle Swarm Optimization.

We also present a procedure for determining the optimal locations of some number of sensors (monitoring wells). Data assimilation is accomplished using a Karhunen-Lo`ve (K-L) parameterization of the geological model, as described e in Sarma et al. (2006). Generalized Pattern Search is applied for the minimization associated with this history matching. The overall set of procedures is applied to a three-dimensional synthetic aquifer model that includes some of the complexities of a realistic site.

• We expand on the work of Chabora & Benson (2009) and Sun & Nicot (2012) to investigate the use of observation wells to detect and locate leaks during the early injection phase of a CCS project. We again apply the K-L parameterization to perform history matching for a variety of leakage scenarios. PSO is used for data assimilation. In this case we seek to characterize the geology of the storage formation and the overlying aquifer, and to determine the location and permeability of some number of leaks in the cap rock. The efficacy of history matching is evaluated for cases using different amounts of observation data.


1.3 Dissertation outline This thesis proceeds as follows. In Chapter 2 we define the general optimization problem and present our methodology for facilitating safe modes of storage and minimizing the risk of leakage in carbon storage applications. We also describe the basic aquifer model which will be used in our examples. Several derivative-free optimization techniques are described, including Hooke-Jeeves Direct Search, Generalized Pattern Search, and Particle Swarm Optimization.

In Chapter 3 we present extensive optimization results for cases where the geology is known. The objective function in most cases is the fraction of mobile CO2 in the formation after 1000 years, though other objective functions and shorter time frames are also considered. Results for optimal injection well positions and well controls for several cases, without and with brine cycling, are provided. We also investigate the sensitivity of optimization results to grid refinement.

In Chapter 4 we apply the key components of the closed-loop optimization methodology to aquifer storage operations where the geological model is uncertain. A new objective function (total CO2 mobility in the top layer, rather than fraction of mobile CO2 ) is used in these optimizations. We provide a description of the major components of the closed-loop framework including a-priori sensor placement optimization and data assimilation using the K-L parameterization. Extensive results for a variety of cases are presented.

In Chapter 5 we describe a new aquifer model, where CO2 may leak through the cap rock into an overlying aquifer. We analyze the degree of CO2 leakage in the model with respect to leak position, leak permeability and other geological features.

We present our history matching algorithm for detecting leaks in the cap rock, and provide results for different leakage scenarios using various amounts of observation data. We also apply a new methodology for determining appropriate data weights for history matching. Our overall analysis allows us to estimate the detectability of leakage conduits using pressure data from injectors and monitoring wells.

In Chapter 6 we provide concluding remarks and some suggestions for future research in this field.


Optimization methodology

In this work, we will apply simulation-based optimization with the objectives of facilitating safer modes of storage and/or reducing the risk of leakage in a storage operation. This could entail minimizing the long-term fraction of mobile CO2 ; i.e., the portion of the sequestered CO2 that can flow in a ‘gas’ phase. Another quantity, which may provide a more direct measure of the risk of leakage through the cap rock, is the total mobility of CO2 that reaches the top of the aquifer. We note that many other formulations, that may also take into account site-specific information, could be used as the objective function in the optimizations.

Optimization entails the determination of optimal placement and control variables (injection rates at a sequence of time periods) for multiple CO2 injection wells to minimize an objective function. In some cases we will incorporate optimization variables governing additional brine injection and production. Such ‘cycling’ events can increase dissolution trapping by exposing CO2 accumulations to brine (see, e.g., Leonenko & Keith, 2008). Residual trapping may also be increased at the interface where CO2 is displaced by injected brine. In optimizations with brine cycling, the optimal time and duration of the cycling events are determined by the optimizer.

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