Facies Modeling Using a Markov Mesh Model Specification
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Facies Modeling Using a Markov Mesh Model Specification Marita Stien · Odd Kolbjørnsen
Received: 28 April 2010 / Accepted: 13 February 2011 / Published online: 27 July 2011 © The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract The spatial continuity of facies is one of the key factors controlling flow in reservoir models. Traditional pixel-based methods such as truncated Gaussian random fields and indicator simulation are based on only two-point statistics, which is insufficient to capture complex facies structures. Current methods for multi-point statistics either lack a consistent statistical model specification or are too computer intensive to be applicable. We propose a Markov mesh model based on generalized linear models for geological facies modeling. The approach defines a consistent statistical model that is facilitated by efficient estimation of model parameters and generation of realizations. Our presentation includes a formulation of the general framework, model specifications in two and three dimensions, and details on how the parameters can be estimated from a training image. We illustrate the method using multiple training images, including binary and trinary images and simulations in two and three dimensions. We also do a thorough comparison to the snesim approach. We find that the current model formulation is applicable for multiple training images and compares favorably to the snesim approach in our test examples. The method is highly memory efficient. Keywords Sequential simulation · Unilateral scan · Generalized linear models 1 Introduction Reservoir models are commonly described by a two-step approach by first defining the geometry of the facies and then populating the model with petrophysical properties (Damsleth et al. 1992). Simulation studies show that the facies model is often one of the main sources of variability in flow (Skorstad et al. 2005). The M. Stien () · O. Kolbjørnsen Norwegian Computing Center, Gaustadalleèn 23, 0314 Blindern, Norway e-mail: [email protected]
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Math Geosci (2011) 43:611–624
spatial distribution of facies is therefore a crucial part of any reservoir model. The use of multi-point statistics for geological facies modeling was proposed nearly two decades ago (Guardiano and Srivastava 1993). Since then, several methods have been developed and tested, along two main paths of development: the statistical modeldriven-approach and the algorithmic approach. Markov random fields (Tjelmeland and Besag 1998) have been the preferred statistical model. The problem with these models is that they are highly time-consuming, both in terms of model estimation and simulation. The development of algorithmically driven methods aims to formulate a simulation procedure that reproduces patterns for a limited template. This approach experienced a break-through with the introduction of search trees (Strebelle 2000). All these methods have been criticized for their lack of consistency, since the statistical model depends on the simulation path
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