Vertical-To-Lateral Transitions Among Cretaceous Carbonate Facies--A Means To 3-D Framework Construction Via Markov Analysis

Abstract

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.

Unravelling the influence of water depth and wave energy on the facies diversity of shelf carbonates

“…Systematic relations that might exist between lateral continuity of facies belts within an EOD would be exciting because they could be used to predict facies extent in outcrops and cores, where one or both of the lateral directions is unsampled, as investigated using Markov chains by Purkis et al . (). Plots of lateral facies extent versus median depth and significant wave height for each facies body do not show strong trends (Figs and ), suggesting no tendency for facies bodies to be systematically larger or smaller in areas of deep water or backwater hydrodynamics.…”

“…If bounded by flooding surfaces, the stack could be termed a ‘parasequence’ and it would be assumed that the lithofacies were deposited in lateral continuity to one another such that Walther's Law holds true (for example, Fig. A); a property that can be harnessed for three‐dimensional reconstruction of carbonate rock bodies (Purkis & Vlaswinkel, ; Purkis et al ., ). The present study was designed to ascertain whether idealized metre‐scale peritidal and subtidal sequences are encountered in two Red Sea focus areas and, if they are, whether the sequences are truly indicative of shallowing‐upward cycles.…”

“…It should be noted that the Markov approach of Bosence () is quite different from that of Rankey () and Purkis et al . (), who employed metrics to estimate the uncertainty in predicting the abundance of facies elements at different water depths. In a study from the Pacific covering an area of 65 km 2 with water depths spanning 0 to 40 m, Purkis & Vlaswinkel () show several facies to inhabit narrow and well‐defined depth regimes, sufficient to be considered non‐random, whereas others could not be constrained so precisely.…”

High-resolution habitat and bathymetry maps for 65,000 sq. km of Earth’s remotest coral reefs

“…With each iteration, the merging decision is based on local homogeneity criteria describing the similarity of adjacent image objects. In a process similar to the annealing function described by Purkis et al (2012b), a cost function is tracked as each merge is conducted and objects cease to be further amalgamated at the point that the function ceases to reduce.…”

Geostatistical modelling of cyclic and rhythmic facies architectures

“…The representation of asymmetry and facies ordering is, however, straightforward in one dimension with Markov chains (Carle and Fogg 1996;Parks et al 2000;Li 2007;Purkis et al 2012) or renewal processes (Matheron 1968), which are based on probabilities of transition between facies, but are difficult to generalise to two or three dimensions. Rhythmicity is another important aspect observed in vertical facies successions.…”