«OPTIMIZATION AND MONITORING OF GEOLOGICAL CARBON STORAGE OPERATIONS A DISSERTATION SUBMITTED TO THE PROGRAM IN EARTH, ENERGY AND ENVIRONMENTAL ...»
Figure 5.15 shows the top layer CO2 saturation at 500 years for the ﬁve true models and their corresponding data-rich and data-scarce history matched solutions.
The data-rich solution generally provides a reasonable estimate of the location of the largest leak, and in some cases also approximately captures the next largest leak. The data-scarce solutions are consistently less accurate in terms of their predictions for leak locations.
The data-scarce scenario does not appear to include suﬃcient observation data to provide accurate predictions for multi-leak cases. The likely cause is that the problem is too under-determined in the data-scarce scenario, with many diﬀerent leakage conﬁgurations able to reproduce the observed pressure in the four sensor wells. Conversely, there are likely fewer leakage conﬁgurations able to reproduce the pressure signals in the nine sensor wells for the data-rich scenario. In future work, it would be useful to quantify the amount of monitoring data required to properly characterize increasingly complicated leakage structures. It will also be important to quantify the uncertainty in our predictions of leakage locations and ﬂuxes. This will, however, require many more data assimilation runs to be performed.
122 CHAPTER 5. LEAKAGE DETECTION FROM HISTORY MATCHING
0.02 Figure 5.15: CO2 saturation at the top of the overlying aquifer after 500 years for MLC1 to MLC5
124 CHAPTER 5. LEAKAGE DETECTION FROM HISTORY MATCHING
5.4 Summary In this chapter we developed and applied computational procedures to analyze CO2 leakage fractions and detect leaks in the cap rock, using pressure data, for a number of leakage cases in carbon storage operations. A three-region model was introduced for these computations. We calculated the CO2 leakage fraction for many leakage cases (some with multiple leaks) to determine the impact of leakage location, leakage grid block permeability, the number of leaks, and geologic heterogeneity. A data assimilation (history matching) procedure, which uses monitoring well pressure data and bottomhole pressure data, was developed with the goal of characterizing leaks.
Aquifer geologies for the storage formation and overlying aquifer were represented using the Karhunen-Lo`ve (K-L) expansion, which signiﬁcantly reduces the number e of geologic variables to be determined in the history match. Particle Swarm Optimization (PSO) was applied for the minimizations required for the data assimilation procedure. A measure for determining the eﬃcacy of history matching for a set of models was developed. This measure was then applied in conjunction with a fast history matching approximation to determine the optimal data weights to be used for data assimilation.
Results from the leakage analysis indicate that the CO2 leakage fraction increases with the leakage block permeability until it plateaus for permeabilities greater than about 2 md. As expected, more leakage was observed when leaks were located above injection wells, or when additional leaks were added. In determining optimal data weights, we found that sensor pressure data in the overlying aquifer were the most important for history matching purposes. Sensor pressure data in the storage formation were next in importance, and bottomhole pressure data from CO2 injection wells provided the smallest beneﬁt to history matching.
Data assimilation results for a number of single-leak and multi-leak cases using both a data-rich scenario and data-scarce scenario provided insight into the detectability of leaks from pressure data. Both the data-rich and data-scarce scenarios resulted in reasonable matches of leak location and CO2 leakage fraction for the single-leak cases that were tested. For multi-leak cases, the CO2 leakage fraction and the location of the largest leaks were matched with some degree of accuracy in the data-rich scenario, whereas the data-scarce scenario provided less accurate predictions.
Summary, conclusions and futurework
In this work we developed and applied computational procedures for optimization and data assimilation (history matching) to minimize the risk of CO2 leakage, track the plume of injected CO2, and detect leaks, in carbon storage operations. The risk of leakage was quantiﬁed both in terms of the mobile CO2 in the storage formation and the total mobility of free CO2 in the top layer of the model. The Hooke-Jeeves Direct Search and Particle Swarm Optimization (PSO) algorithms were used to determine the optimal CO2 injection well locations and time-varying injection rates that minimized the risk of leakage in several examples, including cases with known and uncertain geology. The optimization of parameters controlling brine cycling (where brine is produced from the bottom of the aquifer and re-injected at the top) was also performed for some examples.
In our data assimilation procedure, the geological variables (e.g., porosity) for the storage aquifer, and for the overlying aquifer in leakage examples, were represented by a small number of parameters through use of a Karhunen-Lo`ve (K-L) expansion.
e Data from monitoring and injection wells provided the measurements to be matched.
For cases with no leakage, the Generalized Pattern Search (GPS) method was used to perform the minimization required to determine the geologic variables. GPS was also applied for the a-priori optimization of the placement of monitoring wells and data weights. The goal of this a-priori optimization was to minimize the expected error 126 CHAPTER 6. SUMMARY, CONCLUSIONS AND FUTURE WORK in predicted top layer CO2 mobility for a set of prior models. PSO was applied for history matching in systems involving leakage through the cap rock. For such cases the data assimilation problem entailed determination of the geological models (K-L parameters) for the storage formation and overlying aquifer, as well as the location and permeability of leaks in the cap rock. Monitoring well locations were speciﬁed in these examples, though a method for determining optimal data weights was developed. The data assimilation procedure was applied for a number of single-leak and multi-leak cases.
The key ﬁndings from this study are as follows:
• The use of optimization was shown to reduce the risks associated with carbon storage operations. For cases without brine cycling, in which the geology was assumed to be known, optimization was performed both to minimize the mobile CO2 in the storage aquifer and to minimize the total mobility of CO2 in the top layer of the model. In the former case, a single model was considered, and the fraction of mobile CO2 after equilibration was reduced from 0.34 (for the reference case) to 0.22 by optimizing injection well locations and rates.
Multiple geological models were considered for the minimization of top layer CO2 mobility, and the reduction in this (average) quantity through optimization was 39%. For cases with brine cycling, an optimal trade-oﬀ curve relating the risk objective (fraction of mobile CO2 or total CO2 mobility in the top layer) to the cost objective (volume of brine cycled) was presented for cases with known geology. This curve deﬁnes the Pareto front for systems subject to brine cycling.
• For cases with uncertain geology, optimizing time-varying CO2 injection rates after wells have been drilled (in a-priori optimal locations) was shown to reduce top layer CO2 mobility by at most 7%. Thus, for the examples considered, the application of closed-loop optimization with wells in a-priori optimal locations does not provide a signiﬁcant reduction in top layer CO2 mobility. This is presumably because the objective function depends more strongly on the well locations than on the well controls. This observation motivates the need for improved a-priori site characterization.
• Data assimilation for examples with no leakage demonstrated that pressure and CO2 breakthrough time measurements from monitoring wells (sensors), combined with bottomhole pressure data from injection wells, can be used to history match the geological model and thus improve estimates of the CO2 plume location over long time scales. In our examples, using history matching with eight optimally placed monitoring wells, the average error in top layer mobility over a 500-year time frame was reduced by 46% relative to the average error from the prior model. The error reduction when suboptimal monitoring well placements and data weights were used was only slightly less (43%), suggesting that, at least over a reasonable range, history matching results are not sensitive to the precise values for these variables.
• Results from our pseudo-history matching analysis, which was used to determine optimal data weights for leakage detection, suggest that pressure data from monitoring wells in the overlying aquifer are most important for determining the location and severity of leaks in the cap rock. Pressure data from monitoring wells in the storage formation were next in importance, followed by bottomhole pressure data from CO2 injector wells.
• In most of the leakage detection examples considered here, we found that using pressure data from nine monitoring wells placed in both the overlying aquifer and storage formation provided reasonable matches for the location and severity (permeability) of the largest leak. In multi-leak cases, useful results were also typically achieved for the second largest leak. When four monitoring wells placed only in the overlying aquifer were used for data assimilation, the leak location and severity was reasonably well matched for cases with one leak. The results for multi-leak cases were however considerably less accurate than those using nine monitoring wells placed in both the overlying aquifer and storage formation.
There are a number of issues in this general area that should be investigated
further. Some speciﬁc suggestions for future research are as follows:
• The impact of including additional physics, such as ﬁne-scale heterogeneity, capillary heterogeneity, and mineral trapping, should be investigated to determine their potential eﬀect on optimization and data assimilation results. It is 128 CHAPTER 6. SUMMARY, CONCLUSIONS AND FUTURE WORK important to recognize, however, that modeling these eﬀects will require much ﬁner grid resolution than was used here. While we did perform some limited optimization using increasing grid resolution, further analysis of grid eﬀects and the potential use of upscaling techniques in the optimizations should be investigated.
• Many diﬀerent optimization procedures can be used for the optimization and data assimilation problems considered here, and other techniques should be assessed. For example, the use of a hybrid global-local search (Isebor et al.,
2013) could be considered for the optimization of well placement and injection rates. Eﬃcient approaches for optimizing over many geological realizations have also been presented (Wang et al., 2012), and it may be useful to apply this type of treatment for carbon storage optimization.
• Other measures for leakage risk and costs could also be included in the optimizations. It may be useful, for example, to incorporate pressure information (e.g., injection pressure or pressure at the cap rock) as a constraint to further reduce risk of leakage. In addition, bi-objective optimization involving leakage risk and some direct measure of cost, which should include both capital and operating expenses, could be investigated.
• Other methods for data assimilation, including techniques that account for geological uncertainty by generating multiple history matched models, should also be assessed. The K-L parameterization applied here is suitable for Gaussian models, but it is not in general appropriate for more complicated geological models such as those characterized by multipoint spatial statistics. Parameterizations for these types of models, as discussed by, e.g., Sarma et al. (2008), could be incorporated into the data assimilation algorithms.
• In the data assimilation procedures presented in this work, we have assumed there is no measurement error or noise in the sensor data. While these may be reasonable assumptions for scoping studies, proper treatment of measurement error and noise should be incorporated. This will enable the history matching problem to be addressed in a formal Bayesian framework.
• In addition to optimizing the locations of monitoring wells, it will also be useful to optimize the number and type of monitoring wells to achieve a desired level of accuracy in the history matched model. This may be accomplished by extending the methods developed in this work, and/or through application of some of the procedures described in Isebor et al. (2013). Other measures for quantifying the eﬃcacy of history matched models, and other approaches for very fast but approximate history matching (both of which are required for optimizing monitoring well locations and data weights), should also be considered.