Markov Chain / Transition Probability Approach for Geo-Cellular Modeling of Carbonate Depositional Geobodies: Proof-of-Concept Markov Random Field Simulator
Brigitte Vlaswinkel, Sam Purkis and Nuno Gracias
Event name: 73rd EAGE Conference and Exhibition - Workshops 2011
Session: WS10: Capturing Realistic Sedimentary Architecture in Geo-cellular Reservoir Models- State of the Art and Advances from Object to Process Modeling, to Multipoint Statistics.
Publication date: 27 May 2011
Info: Extended abstract, PDF ( 436.34Kb )
Price: € 20
A reservoir model based on subsurface data as well as appropriate (reservoir) analogs is a critical field management tool, and therefore should accurately incorporate features affecting fluid storage, distribution and flow. However, the complexity of specifically carbonate reservoirs makes detailed direct-characterisation of their 3D heterogeneity difficult, and this problem is worsened in the subsurface where lateral constraint on facies architecture is typically poor to non-existent, while information on vertical stacking maybe rich. A tantalizing strategy to mitigate this disjoint lies in the use of Walther’s Law, which offers the possibility of using vertical transitions to elucidate lateral juxtaposition motifs (Doveton 1994; Parks et al. 2000; Elfeki & Dekking 2005; Riegl & Purkis 2009). The implication being that a reservoir model, competent at least in terms of transition statistics, could be built against information harvested down-core. Coupled with simple Markov theory, it can be deduced that under such conditions, comparable facies frequencies and transition probabilities will link vertical and lateral facies stacks. If one can be quantified, the other can be solved for. It therefore follows that 2D or even 3D Markov chain models can be developed by assuming that spatial variability in any direction can be characterised by a 1D Markov chain. Although this may seem like a tenuous theoretical leap, the assumption here is merely that Markov chains might characterise spatial variability not only in the vertical but in other stratigraphic directions such as dip or strike (Carle et al. 1998). In this paper we present a proof-of-concept Markov Random Field Simulator (MRFS) and test its 3D geo-cellular modelling capabilities against a Cretaceous carbonate outcrop dataset. The assumption Walther’s Law can be applied has been verified successfully beforehand, based on two case studies that call upon (carbonate) data from the Cretaceous, Miocene and Modern (Purkis et al., submitted).