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Using DoE Methodology to Evaluate Uncertainty of CO 2 Storage in Saline Aquifers

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## Using DoE Methodology to Evaluate Uncertainty of CO 2 Storage in Saline Aquifers

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**Using DoE Methodology to Evaluate Uncertainty of CO2 Storage**in Saline Aquifers Paul Liu and Linda Zhang 01/21/2011**Introduction**• Challenges in CO2 storage in saline aquifers • Reservoir characterization data are scarce • Reservoirs are heterogeneous • Financial constraints (Cost center) • A variety of stratigraphic models are built based on available data**Introduction**• Questions • What are the necessary/important data to modeling CO2 storage in saline aquifers? • Can stratigraphic models capture the flow behaviors of the heterogeneous aquifer? • Is there a most optimal stratigraphic model capable of functioning as the heterogeneous aquifer?**Objectives**• Identify the most important parameters which impact the prediction of CO2 in a fully heterogeneous aquifer model (FHM) over time • Evaluate if stratigraphic models are able to identify those important parameters as identified by the FHM • Assess the uncertainty predicted by both the FHM and stratigraphic models. • Determine the most optimal stratigraphic model to CO2 storage modeling**Approaches**• Upscaling permeability for a synthetic aquifer multiple stratigraphic models of decreasing complexity multiple conceptual models at a given field site; • DoE & RS modeling: conduct a parameter SA & prediction uncertainty analysis for all models, based on the same set of uncertain input parameters; • Within a full parameter space, evaluate each stratigraphic model against the parameter sensitivity & prediction uncertainty of the FHM; • Multiple simulation outcomes are evaluated, over increasingly longer times (injection, monitoring);**Saline Storage Model**Populate aquifer with the 4 conceptual models (aquitard is assumed homogeneous): ETC-Quantitative Stratigraphy**FHM and Conceptual Models**FHM 8-Unit 1-Unit 3-Unit**Model Parameters**• Saline aquifer size (L: 2025 m; W: 2025 m; T: 102.5 m) • Caprock thickness: 40 m • Model blocks: 101*101*(10+41)=520251 • Well is located in the geographic center, and perforated fully in the aquifer only • 20-40 years of injection, followed with 500 yrs of monitoring.**Model Parameters**• Initial condition: hydrostatic pressure • Boundary conditions: open side boundary; downward/upward hydraulic gradient is established by setting a top or bottom aquifer. • Reservoir Temperature: constant • Brine density is homogenous • Model depth: 1 km, 2 km, and 3 km**Modified from data that Bennion and Bachu’s publications:**SPE 99326 & SPE 106995;**Design of Experiment**• Def: statistical design of experiment refers to the process of planning the experiment so that appropriate data that can be analyzed by statistical approach will be collected, resulting in valid and objective conclusions. (Montgomery, 2005) • The statistical approach to experimental design is necessary if we wish to draw meaningful conclusions from data. (Montgomery, 2005)**Design of Experiment**Full factorial design**PB Design & RS Methodology**• PB designs are two level fractional factorial designs for studying k=N-1 variables in N runs, where N is a multiple of 4. (Montgomery, 2005) • PB designs are used for screening experiments when only main effects are considered significant. Two-factor interactions are heavily confounded with main effects. • RSM, is a collection of mathematical and statistical techniques useful for the modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response. (Montgomery, 2005)**Variables and Responses**AquG: vertical aquifer hydraulic gradient; TG: geothermal gradient; VAR: s2lnk (aquifer); SGR: Sgr (residual gas saturation) SAL : brine salinity; q: CO2 injection rate; krock: caprock permeability • Responses • Mobile gas amount; • Trapped gas amount; • Dissolved gas amount; • Brine displaced out of the caprock; • Gas leaked out of the caprock.**Results and Discussions**SGR, VAR, SAL are identified as the most important factors.**Performances of Models**Mobile gas Trapped gas Dissolved gas**Performances of Models**Mobile gas Trapped gas Dissolved gas**Use Response Surface Methodology to Evaluate Uncertainty**Range**Use Response Surface Methodology to Evaluate Uncertainty**Range**Use Response Surface Methodology to Evaluate Uncertainty**Range**Conclusions**• SGR, VAR, SAL are three most important factors to modeling CO2 storage in saline aquifers. • Stratigraphic models are generally capable of capturing the important factors identified by the FHM. • In the full parameter space tested, depositional and facies models are nearly equally accurate in predicting gas profiles, plume shape, and brine leakage of the FHM. The optimal model is the depositional model. • When aquifer heterogeneity is low, homogeneous formation model works fine. • To assess the security of caprock, the homogeneous formation model works fine, regardless of aquifer heterogeneity. • Above results are not sensitive to depth.**Ongoing Project**• Build geological model for the Mt. Simon aquifer; • Apply DoE into this practice. • The challenges are: how to quantify geological and petrophysical uncertainties?**Collected Data1) Only a few of wells have logs of Mt.**Simon;2) Top and base contour maps;3) Isopach map of Mt. Simon;4) Salinity contour map;5) Structure features;6) ADM site data is confidential. ETC-Quantitative Stratigraphy