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1 Introduction

Injection of carbon dioxide (CO2) into deep saline aquifers is considered a promising option to mitigate global climate change. To assess the appropriateness of a storage site, reservoir simulation is commonly performed. As part of the simulation workflow, a site geologic model must be built. However, data needed to build a detailed geologic model are often unavailable. As a compromise, stratigraphic models are built in which facies or depositional zones, or even the entire aquifer, are assumed homogeneous. Since natural aquifers exhibit permeability heterogeneity at multiple scales, stratigraphic models are conceptual simplifications made at complexities appropriate for the levels of data support. It is important to understand not only the adequacy of such models in representing natural systems, but also if an optimal complexity in stratigraphic model exists that can lead to a cost-effective strategy in data collection and reservoir modeling. However, a key difficulty exists in addressing this problem: in addition to uncertainty in aquifer permeability, uncertainty in multiple geologic and engineering variables also exists. Determination of an optimal stratigraphic model must be evaluated within the full parameter space, which is computationally demanding for CO2 storage modeling.

In this study, a design of experiment (DoE) and response surface (RS) methodology is used to conduct a parameter sensitivity study and associated prediction uncertainty analysis. This method is computationally efficient, particularly suitable for analyzing data-poor settings with many sources of uncertainty. To eliminate uncertainty in permeability pattern and only focus on parameter uncertainty, a synthetic aquifer is created to represent a groundtruth model with fully known permeability. This fully heterogenous model (FHM) is used to gauge the performance of 3 stratigraphic models of decreasing complexities. Since aquifers can exhibit different degrees of permeability heterogeneity, the FHM is scaled to increasing natural log permeability (lnk) variance.

For this set of models (i.e., stratigraphic models are conceptual equivalents of the FHM), multiple uncertain input variables are defined, their selection based on typical uncertainty parameters and their ranges that can be encountered at a CO2 storage site. For a suite of prediction outcomes, a stratigraphic model is considered optimal for predictions if it can capture both the parameter sensitivity and prediction uncertainty of the FHM. Specifically, within the full parameter space, the stratigraphic models are examined in 3 aspects: (1) accuracy in predicting CO2 mass profiles, plume shape, and brine leakage; (2) ability to capture the most important parameters that impact the outcomes of the FHM; (3) for the same outcomes, ability to capture the prediction envelopes of the FHM.

Further, worldwide saline aquifers suitable for CO2 storage can be found at a range of depths. To explore the effect of depth on model sensitivity and prediction uncertainty, the models are placed at depths of 1, 2, and 3 km, respectively. The uncertainty analysis is repeated at each depth.

2. Method

2.1 Experimental Stratigraphy

Using detailed images of an experimental stratigraphy, a FHM is created exhibiting permeability heterogeneity. Using facies analysis, a stratigraphic model is created containing 8 facies units. Since the flume deposit emulates a fluvial system with multiple depositional episodes, a 3-Unit layered model is created, with each layer consisting of several units of the facies model. A geological formation model is also created, containing a single unit. The stratigraphic models are hosted within a sedimentary hierarchy, representing conceptual models developed at decreasing complexity from full heterogeneity. To ensure that models are comparable, equivalent permeability is computed for each unit of the stratigraphic models using a numerical upscaling technique that the PI has developed.

2.2 CO2 Simulation

CO2 simulation is conducted using GASWAT of ECLIPSE 300. A single vertical injection well is placed at the center of the model. Injection duration lasts from 20-40 years, corresponding to changing injection rate. A 500-year post-injection monitoring period is modeled.

2.3 Sensitivity Analysis (SA) & Response Surface (RS) Modeling

A SA analysis is conducted based on a Plackett-Burman (PB) design of Expreiment (DoE). For each model, simulations are conducted according to the PB design. Select outcomes are compiled. For each outcome, parameter importance is determined by MANOVA. RS modeling is then conducted. A RS is a polynomial function of the important factors that impact a model outcome. These factors are identified by the PB design. Using RS, a range of predictions can be made by varying the important factors within their respective ranges. RS-predicted outcomes represent new responses that have not been simulated. Since prediction using RS is fast, it is used as a proxy for reservoir simulation to efficiently analyze prediction uncertainty.

3. Results

Results suggest that for the parameter space considered in this study, facies and layered models are capable of capturing the most important sensitivity parameters of the FHM. The same two models also capture the ranges of predictions in mobile gas, trapped gas, and brine leakage. The formation model is less accurate in capturing the sensitivity and prediction ranges of the FHM, but is accurate in predicting brine leakage. Thus, optimal model complexity is affected by the type of prediction metric of interest. In predicting gas flow and storage, the layered model appears optimal; in predicting brine leakage (which is related to fluid pressure), the formation model appears optimal.

Further, model sensitivity and prediction uncertainty are not affected greatly by depth. At all the depths tested, for multiple outcomes and over multiple time scales, all stratigraphic models are able to capture the most significant uncertainty parameter that impacts the predictions of the FHM. Thus, when stratigraphic models are assigned equivalent permeabilities, parameter sensitivity evaluated using these models can be useful to identify the most important variable that impacts predictions. In this study, the FHM is known a priori, thus equivalent permeability is obtained using upscaling. In modeling natural systems, inverse calibration technique is needed to obtain an optimal permeability for the stratigraphic models that will approach the equivalent permeability. 

Details of the results are presented in a manuscript, currently in review, with the Environmental Science & Technology.