Fluid Pressure Redistribution Events Within a Fault: Impact of Material Property Correlation
Cellular automata (CA) models employ local rules to simulate large-scale behavior. A previously developed CA model of fluid pressure redistribution events within a 2D planar fault system undergoing compression is used to model the size distribution of these events over time. Local fluid pressures exceeding a threshold value cause a rupture (failure) of the surrounding rock, and the fluid pressure is redistributed to surrounding cells. Spatial correlation of the fault compressibility (β) is varied over a range of nearly three orders of magnitude in a model domain of 106 cells. The size distribution of all pressure redistribution events changes from a power-law exponential form with a single slope when β is uncorrelated to a power-law exponential form with two slopes at increasing correlation lengths and then back to a single power-law exponential distribution that approximates a uniform distribution as correlation lengths exceed the ergodic limit. The spatially and temporally uniform pattern of events seen in the uncorrelated model rapidly evolve to exhibit emergent behavior as the correlation length increases beyond the grid cell size. Increasing spatial correlation leads to delays in the time to first failure and decreases the time necessary for the ruptures to coalesce and span the fault domain. The resulting spatial pattern of events demonstrates deviations from the random point process associated with uncorrelated β towards increased spatial clustering of events with increasing correlation of the β field. Vertical effective permeability of the fault system at the point where connected failures span the domain shows that effective permeability is a nonlinear function of the correlation length and is strongly controlled by the size (area) of the domain-spanning failed cluster.
KeywordsSpatial Correlation Correlation Length Cellular Automaton Effective Permeability Cellular Automaton Model
This material is based upon work supported as part of the Center for Frontiers of Subsurface Energy Security, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001114. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04–94AL85000.
- Cowie PA, Vanneste C, Sornette D (1993) Statistical physics model for the spatiotemporal evolution of faults. J Geophys Res 98(B12):21,809–21,821Google Scholar
- Diggle PJ (2003) Statistical analysis of spatial point patterns, 2nd edn. Oxford University Press, OxfordGoogle Scholar
- MATLAB (2011) The MathWorks Inc., version 7.13.0, Natick, MassachusettsGoogle Scholar
- Miller SA, Nur A (2000) Permeability as a toggle switch in fluid-controlled crustal processes. Earth Planet Sci Lett 183(133):146Google Scholar
- Mitchell M (2009) Complexity: a guided tour. Oxford University Press, Oxford, 349 pGoogle Scholar
- Stauffer D, Aharony A (1994) Introduction to percolation theory, revised 2nd edition. Taylor and Francis Inc., Philadelphia, 181pGoogle Scholar
- Zhang H (1999) On the ergodicity hypothesis in heterogeneous formations. Math Geol 31(1): 113–134Google Scholar
- Zoback MD, Harjes HP (1997) Injection-induced earthquakes and crustal stress at 9 km depth at the KTB deep drilling site, Germany. J Geophys Res Solid Earth 102:18,477–18,491Google Scholar