Geostatistical Models of Secondary Oil Migration Within Heterogeneous Carrier Beds: A Theoretical Example

Abstract

This paper critically evaluates the utility of two different geostatistical methods in tracing long-distance oil migration through sedimentary basins. Geostatistical models of petroleum migration based on kriging and the conditional simulation method are assessed by comparing them to known oil migration rates and directions through a numerical carrier bed. In this example, the numerical carrier bed, which serves as ground truth in the study, incorporates a synthetic permeability field generated using the method of turning bands. Different representations of lateral permeability heterogeneity of the carrier bed are incorporated into a quasi-three-dimensional model of secondary oil migration. The geometric configuration of the carrier bed is intended to represent migrat on conditions within the center of a saucer-shaped intracratonic sag basin. In all of the numerical experiments, oil is sourced in the lowest 10% of a saucer-shaped carrier bed and migrates 10-14 km outward in a radial fashion by buoyancy. The effects of vertical permeability variations on secondary oil migration were not considered in the study. Two sets of numerical experiments are presented in this study. In the first set, computed oil migration patterns and rates through the numerical carrier bed are compared to kriged and optimal estimations based on a suite of 50 conditional simulations to determine the utility of each geostatistical approach. The geostatistical models also are compared to a much simpler oil migration simulation using a homogeneous carrier bed, an assumption typically made in cross sectional models of oil migration. The permeability realizations generated by kriging and the conditional simulation method were constructed using 50 randomly placed sampling points. A second set of numerical experiments was made to determine how data sample size (20, 35, 50, 100, and 250 randomly selected points) influences p edicted oil migration patterns using kriged permeability fields. Oil migration patterns through the synthetic carrier bed were quantitatively compared to geostatistical representations of oil transport by computing the degree of correlation (r2) of oil lens thickness at 5, 10, and 15 m.y. after the onset of migration. Quantitative results indicate that both kriging and the conditional simulation method produced realistic representations of spatial oil lens patterns and first arrival times. Both kriging and the conditional simulation method produced results far more realistic than the simulation with a homogeneous carrier bed. After 15 m.y., the spatial correlations (r2) between the known oil lens patterns and that of the kriged and ensemble average of the 50 conditional simulations were 0.67 and 0.74, respectively. Although the conditional simulation method produced the best results, it did so at a significant computational expense. Computed oil migration patterns based on different kriged permeability maps that incorporated varying amounts of control data points did not improve signif cantly when more than 100 randomly placed wells were used. The study provides compelling evidence that secondary oil migration is an inherently three-dimensional process. For well-studied basins, geostatistical representations of long-range oil migration could be of value in ongoing exploration strategies. End_Page 1679------------------------------