Semi-Analytic Modelling of Subsidence
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Semi-Analytic Modelling of Subsidence1 Peter A. Fokker2 and Bogdan Orlic2 This paper presents a forward model for subsidence prediction caused by extraction of hydrocarbons. The model uses combinations of analytic solutions to the visco-elastic equations, which approximate the boundary conditions. There are only a few unknown parameters to be estimated, and, consequently, calculations are very fast. The semi-analytic model is applicable to a uniform and layer-cake stratigraphy, with visco-elastic parameters changing per layer, and an arbitrary depletion pattern. By its capabilities to handle a multi-layered visco-elastic subsurface, the semi-analytic model fills the gap between the analytic single-layered elastic models available to date and the more elaborate numerical, e.g. finite element, models. KEY WORDS: subsidence, reservoir compaction, geomechanics, semi-analytic model, viscoelasticity.
INTRODUCTION Production of hydrocarbons reduces the reservoir pressure. This pressure change affects the in-situ stress field through poro-elastic coupling. The reservoir may compact, resulting in land subsidence or seabed subsidence. Classical examples are the Wilmington oil field in California (Mayuga and Allen, 1969), the Ekofisk oil field in chalk in the Norwegian sector of the North Sea (Nagel, 1998) and the Groningen gas field in the northern part of the Netherlands (Doornhof, 1992; Houtenbos, 2000). Rate of compaction at reservoir level and surface subsidence are mutually dependent. Forward modelling can be used if the amount of reservoir compaction is known, or if it can be predicted to an acceptable confidence level, and when existing or future subsidence has to be estimated. Various authors have studied the subsidence caused by hydrocarbon extraction and proposed methods for subsidence prediction. Geertsma (1973) was the first to apply an analytic, linear forward model, based on the nucleus of strain concept, for a single-layer elastic subsurface. Others have expanded his formulae, 1Received
26 August 2004; accepted 8 December 2005; Published online: 2 November 2006. Institute of Applied Geoscience TNO – National Geological Survey, P.O. Box 80015, 3508 TA Utrecht, The Netherlands; e-mail: [email protected]; [email protected].
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565 C 2006 International Association for Mathematical Geology 0882-8121/06/0700-0565/1
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or presented alternatives. Van Opstal (1974) included the effects of a rigid basement. Fares and Li (1988) presented a general image method for a plane-layered elastic medium, which involves infinite series of images. Both analytic solutions are, however, limited to media with two interfaces and therefore to a two-layer model of the subsurface. A different approach is the use of numerical codes, such as finite elements (Morita and others, 1989; Johnson and others, 1989; Fredrich and others, 1998; Chin and Thomas, 1999). These enable simulation of the full relationship between flow in the porous medium and geomechanics, taking into account complex structural geo
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