Time-dependent Inversion of Surface Subsidence due to Dynamic Reservoir Compaction
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Time-dependent Inversion of Surface Subsidence due to Dynamic Reservoir Compaction A.G. Muntendam-Bos · I.C. Kroon · P.A. Fokker
Received: 9 January 2007 / Accepted: 11 August 2007 / Published online: 24 January 2008 © International Association for Mathematical Geology 2008
Abstract We introduce a novel, time-dependent inversion scheme for resolving temporal reservoir pressure drop from surface subsidence observations (from leveling or GPS data, InSAR, tiltmeter monitoring) in a single procedure. The theory is able to accommodate both the absence of surface subsidence estimates at sites at one or more epochs as well as the introduction of new sites at any arbitrary epoch. Thus, all observation sites with measurements from at least two epochs are utilized. The method uses both the prior model covariance matrix and the data covariance matrix, which incorporates the spatial and temporal correlations between model parameters and data, respectively. The incorporation of the model covariance implicitly guarantees smoothness of the model estimate, while maintaining specific geological features like sharp boundaries. Taking these relations into account through the model covariance matrix enhances the influence of the data on the inverted model estimate. This leads to a better defined and interpretable model estimate. The time-dependent aspect of the method yields a better constrained model estimate and makes it possible to identify non-linear acceleration or delay in reservoir compaction. The method is validated by a synthetic case study based on an existing gas reservoir with a highly variable transmissibility at the free water level. The prior model covariance matrix is based on a Monte Carlo simulation of the geological uncertainty in the transmissibility. Keywords Subsidence · Compaction · History matching · Covariance · Inversion A.G. Muntendam-Bos () · I.C. Kroon · P.A. Fokker TNO Built Environment and Geosciences, Princetonlaan 6, P.O. Box 80015, Utrecht 3508 TA, The Netherlands e-mail: [email protected] I.C. Kroon e-mail: [email protected] P.A. Fokker e-mail: [email protected]
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Math Geosci (2008) 40: 159–177
1 Introduction Surface subsidence has important social repercussions, due to the associated risks of damage to buildings and infrastructure. In the Netherlands, a country protected by dykes because about 60% of the area is below sea level (Bremmer et al. 2003), land subsidence is of great concern because it increases the risk of flooding and has implications for groundwater management. It is exacerbated by developments like urbanization, intensification of subsurface use, sea level rise, and an increase in intensive rainstorms. The safety and financial impacts are such that even subsidence of the order of centimeters may raise major concerns. As an example, the exploitation of the large Groningen gas field in the northern Netherlands has produced subsidence of at least 20 cm (Doornhof 1992). The four most common methods used to measure surface displacement over time are optical instrument l
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