The search for, and extraction of, hydrocarbons in carbonate rocks demands a thorough understanding of their depositional anatomy. The complexity of carbonate systems, however, hinders detailed direct characterization of their volumetric heterogeneity. Information with which to construct a reservoir model must therefore be based on information gathered from wells or outcrops transecting the sequence of interest. Most (particularly exploration wells) are vertical, presenting a problem for geostatistical modeling. While understanding vertical stratal stacking is straightforward, it is difficult to obtain lateral facies information. Though in some situations outcrop surfaces, seismic data, and horizontal wells may somewhat mitigate this bias, the likelihood remains that the lateral dimension of a buried system will be vastly undersampled with respect to the vertical. However, through the principle of Walther's Law (Walther 1894) or due to the geometry of basinward-inclined beds, comparable facies frequencies and transition probabilities may link vertical and lateral stratal arrangements, the implication being that a reservoir model, competent at least in terms of transition statistics, could be built against information harvested down-core. Taking an interpreted outcrop panel from Lewis Canyon (Albian, Pecos River, Texas), we use Markov-chains to first ascertain that vertical and lateral stratal ordering is nonrandom. Second, we show lithofacies transition probabilities in the outcrop as being interchangeable between the vertical and lateral directions. The work concludes by demonstrating the utility of an existing 3-D Markov random field simulation to volumetrically model the Lewis Canyon outcrop on the basis of vertical facies transition tendencies. Statistical interrogation of the 3-D model output reveals the simulation to contain realistic facies associations compared to the outcrop. This suggests that the reconstruction process, based on Markov chains, produces a useful representation of 3-D heterogeneity in this Lower Cretaceous carbonate succession. Markov random field simulation might provide an important tool for prediction and simulation of subsurface carbonate reservoirs.
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