Bayesian inversion is performed on real observations to predict the diagenetic classes of a carbonate reservoir where the proportions of carbonate rock and depositional properties are known. The complete solution is the posterior model. The model is first developed in a 1D setting where the likelihood model is generalized Dirichlet distributed and the prior model is a Markov chain. The 1D model is used to justify the general assumptions on which the model is based. Thereafter the model is expanded to a 3D setting where the likelihood model remains the same and the prior model is a profile Markov random field where each profile is a Markov chain. Lateral continuity is incorporated into the model by adapting the transition matrices to fit a given associated limiting distribution, two algorithms for the adjustment are presented. The result is a good statistical formulation of the problem in 3D. Results from a study on real observations from a 2D reservoir show that simulations reproduce characteristics of the real data and it is also possible to incorporate conditioning on well observations into the model.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:ntnu-11244 |
| Date | January 2010 |
| Creators | Larsen, Elisabeth Finserås |
| Publisher | Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, Institutt for matematiske fag |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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