Oil-gas reservoir lithofacies stochastic modeling based on one- to three-dimensional Markov chains

Stochastic modeling techniques have been widely applied to oil-gas reservoir lithofacies. Markov chain simulation~ however~ is still under development~ mainly because of the difficulties in reasonably defining conditional probabilities for multi-dimensional Markov chains and determining transition probabilities for horizontal strike and dip directions. The aim of this work is to solve these problems. Firstly~ the calculation formulae of conditional probabilities for multi-dimensional Markov chain models are proposed under the full independence and conditional independence assumptions. It is noted that multi-dimensional Markov models based on the conditional independence assumption are reasonable because these models avoid the small-class underestimation problem. Then~ the methods for determining transition probabilities are given. The vertical transition probabilities are obtained by computing the transition frequencies from drilling data~ while the horizontal transition probabilities are estimated by using well data and the elongation ratios according to Walther＇s law. Finally~ these models are used to simulate the reservoir lithofacies distribution of Tahe oilfield in China. The results show that the conditional independence method performs better than the full independence counterpart in maintaining the true percentage composition and reproducing lithofacies spatial features.

A note on testing conditional independence for social network analysis

In social network analysis, logistic regression models have been widely used to establish the relationship between the response variable and covariates. However, such models often require the network relationships to be mutually independent, after controlling for a set of covariates. To assess the validity of this assumption,we propose test statistics, under the logistic regression setting, for three important social network drivers. They are, respectively, reciprocity, centrality, and transitivity. The asymptotic distributions of those test statistics are obtained. Extensive simulation studies are also presented to demonstrate their finite sample performance and usefulness.

Point process models, the dimensions of biodiversity and the importance of small-scale biotic interactions

Aims Recent mechanistic explanations for community assembly focus on the debates surrounding niche-based deterministic and dispersalbased stochastic models.This body of work has emphasized the importance of both habitat filtering and dispersal limitation,and many of these works have utilized the assumption of species spatial independence to simplify the complexity of the spatial modeling in natural communities when given dispersal limitation and/or habitat filtering.One potential drawback of this simplification is that it does not consider species interactions and how they may influence the spatial distribution of species,phylogenetic and functional diversity.Here,we assess the validity of the assumption of species spatial independence using data from a subtropical forest plot in southeastern China.Methods We use the four most commonly employed spatial statistical models—the homogeneous Poisson process representing pure random effect,the heterogeneous Poisson process for the effect of habitat heterogeneity,the homogenous Thomas process for sole dispersal limitation and the heterogeneous Thomas process for joint effect of habitat heterogeneity and dispersal limitation—to investigate the contribution of different mechanisms in shaping the species,phylogenetic and functional structures of communities.Important Findings Our evidence from species,phylogenetic and functional diversity demonstrates that the habitat filtering and/or dispersal-based models perform well and the assumption of species spatial independence is relatively valid at larger scales(50×50 m).Conversely,at local scales(10×10 and 20×20 m),the models often fail to predict the species,phylogenetic and functional diversity,suggesting that the assumption of species spatial independence is invalid and that biotic interactions are increasingly important at these spatial scales.