2. DATA AND METHODLOLOGY
2.4. MONTE CARLO SIMULATIONS:
The study presented in Chapter 3 focuses on taking the geological information collected via the above methods, and making an assessment on the uncertainty in calculating potential CO2 storage capacity derived from this information. For this purpose, Monte Carlo forecasting methods are employed to simulate capacity based upon a defined range of input values. Monte Carlo simulations are a commonly used method and are well documented in literature. As such, a brief summary will be presented here, however for further information the reader is directed to Metropolis (1987), Kroese et al. (2013) and Rubinstein and Kroese (2011).
2.4.1. THEORY AND HISTORY OF THE MONTE CARLO METHOD
The Monte Carlo method was conceived as a consequence of the Manhattan Project by mathematicians Stanislaw Ulam and Jon von Neumann as a statistical approach to solving the problem of neutron diffusion in fissionable materials (Metropolis, 1987; Metropolis and Ulam, 1949). At the centre of the Monte Carlo method is a statistical decisions based upon repeat random sampling in order to solve a mathematical or statistical problem (Sawilowsky, 2003). For geostatistical uses, the user may define end and or mid points for a specific function within the problem, and the random numbers will be generated based upon a probability distribution therein. For example, a normal distribution is a function that defines
51 the probability of a number that occurs between two real numbers, such as measured minimum and maximum values (Davis, 1986).
The Monte Carlo simulations performed in this study were carried out using the Oracle Crystal Ball software. This software is a Microsoft Excel based suite of analytical tools capable of Monte Carlo simulation, forecasting and optimisation.
The software is in common usage amongst the oil and gas sector for the forecasting of reserves and the assessment of risk, both technical and financial. Specific to this study is the software’s ability to perform sensitivity analysis on the inputted data in order to determine which of the input variables drives the uncertainty of the reserve estimate models. These data are presented in the form of tornado diagrams, a style of bar chart that divides data categories vertically, and ordered such that the largest bar appears at the top, decreasing downwards to the smallest.
The simulations performed in this study utilised input data collated from a wider range of sources from published literature to measured downhole geological parameters. The lack of data availability directly over the study site required use of regional analogues, where geological variability necessitates the data to be presented as ranges rather than finite values. For use in Crystal Ball, these ranges must be assigned a suitable probability distribution, such that the generation of random numbers best fits the range and any skew in the data. The justifications behind the exact distributions used in this study are presented in Chapter 3, and the raw outputted report is included in Appendix 1b.
52 REFERENCES
Asquith, G. B., and Gibson, C. R., 1982, Basic Well Log Analysis for Geologists, Tulsa, Oklahoma, The American Association of Petroleum Geologists.
Bacon, M., Simm, R., and Redshaw, T., 2003, Three-‐D Seismic Interpretation, Cambridge University Press.
Brown, A. R., 2004, Interpretation of Three-‐dimensional Seismic Data, American Association of Petroleum Geologists and the Society of Exploration Geophysicists, v. no. 42.
Cairns, G., Jakubowicz, H., Lonergan, L., and Muggeridge, A., 2012, Using time-‐lapse seismic monitoring to identify trapping mechanisms during CO2 sequestration: International Journal of Greenhouse Gas Control, v. 11, no. 0, p. 316-‐325.
Cartwright, J., 2007, The impact of 3D seismic data on the understanding of compaction, fluid flow and diagenesis in sedimentary basins: Journal of the Geological Society, v. 164, no. 5, p. 881-‐893.
Chadwick, R. A., Noy, D., Arts, R., and Eiken, O., 2009, Latest time-‐lapse seismic data from Sleipner yield new insights into CO2 plume development: Energy intrusions primed by silica diagenesis: Geology, v. 34, no. 11, p. 917-‐920.
Davies, R. J., Thatcher, K. E., Armstrong, H., Yang, J., and Hunter, S., 2012, Tracking the relict bases of marine methane hydrates using their intersections with stratigraphic reflections: Geology, v. 40, no. 11, p. 1011-‐1014.
Davis, J. C., 1986, Statistics and Data Analysis in Geology, New York, John Wiley &
Sons, Inc.
Emery, D., Myers, K., and Bertram, G. T., 1996, Sequence Stratigraphy, Wiley.
Ireland, M. T., Goulty, N. R., and Davies, R. J., 2011, Influence of stratigraphic setting and simple shear on layer-‐bound compaction faults offshore Mauritania:
Journal of Structural Geology, v. 33, no. 4, p. 487-‐499.
Kearey, P., Brooks, M., and Hill, I., 2009, An Introduction to Geophysical Exploration, Wiley.
Koyi, H., Talbot, C. J., and Torudbakken, B. O., 1995, Analogue models of salt diapirs and seismic interpretation in the Nordkapp Basin, Norway: Petroleum Geoscience, v. 1, no. 2, p. 185-‐192.
Kroese, D. P., Taimre, T., and Botev, Z. I., 2013, Handbook of Monte Carlo Methods, Wiley.
Metropolis, N., 1987, The beginning of the Monte Carlo method: Los Alamos Science, v. 15, no. 584, p. 125-‐130.
Metropolis, N., and Ulam, S., 1949, The monte carlo method: Journal of the American statistical association, v. 44, no. 247, p. 335-‐341.
53 Mouchet, J.-‐P., and Mitchell, A., 1989, Abnormal pressures while drilling: Origins -‐
Prediction -‐ Dectection -‐ Evaluation, elf aquitaine: manuels techniques.
Nguyen, J.-‐P., 1996, Drilling: Oil and Gas Field Development Techniques, Institut Francais du Petrole Publications: Editions Technip.
Posamentier, H. W., Davies, R. J., Cartwright, J. A., and Wood, L., 2007, Seismic geomorphology -‐ an overview: Geological Society, London, Special Publications, v. 277, no. 1, p. 1-‐14.
Rubinstein, R. Y., and Kroese, D. P., 2011, Simulation and the Monte Carlo Method, Wiley.
Sawilowsky, S. S., 2003, You think you've got trivials: Journal of Modern Applied Statistical Methods, v. 2, no. 1, p. 218-‐225.
Sheriff, R. E., and Geldart, L. P., 1982, Exploration Seismology: History, theory, &
data acquisition, Cambridge University Press, v. v. 1.
-‐, 1995, Exploration Seismology, Cambridge University Press.
Taylor, M. H., Dillon, W. P., and Pecher, I. A., 2000, Trapping and migration of methane associated with the gas hydrate stability zone at the Blake Ridge Diapir: new insights from seismic data: Marine Geology, v. 164, no. 1–2, p.
79-‐89.
Vail, P. R., Mitchum, R. M., and Thompson, S., 1977, Seismic stratigraphy and global changes of sea level, part 4: global cycles of
relative changes of sea level, in Payton, C. E., ed., Seismic Stratigraphy: Applications to Hydrocarbon Exploration, Volume 26: Tulsa, American Association of Petroleum Geologists, p. 83-‐97.
Weimer, P., and Davis, T., 1996, Applications of 3-‐D seismic data to exploration and production: AAPG Studies in Geology 42: SEG Geophysical Development Series, v. 5, p. 270.
White, D., 2013, Seismic characterization and time-‐lapse imaging during seven years of CO2 flood in the Weyburn field, Saskatchewan, Canada:
International Journal of Greenhouse Gas Control, v. 16, Supplement 1, no. 0, p. S78-‐S94.
Wright, K. A., Davies, R. J., Jerram, D. A., Morris, J., and Fletcher, R., 2012, Application of seismic and sequence stratigraphic concepts to a lava-‐fed delta system in the Faroe-‐Shetland Basin, UK and Faroes: Basin Research, v.
24, no. 1, p. 91-‐106.
Yilmaz, Ö., and Doherty, S. M., 1987, Seismic Data Processing, Society of Exploration Geophysicists.
Zoeppritz, K., 1919, Erdbebenwellen VII. VIIb. Über Reflexion und Durchgang seismischer Wellen durch Unstetigkeitsflächen: Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-‐
physikalische Klasse, p. 66-‐84.
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