--> Pore Pressure Modeling Using Multivariate Geostatistics

AAPG Asia Pacific Region GTW, Pore Pressure & Geomechanics: From Exploration to Abandonment

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Pore Pressure Modeling Using Multivariate Geostatistics

Abstract

Sedimentary basins are subject to pore pressure anomalies caused by subcompaction mechanisms, fluid expansion, hydrocarbon generation and tectonism. In this context, multivariate geostatistical pore pressure modeling has attracted the attention of geoscientists and engineers as a framework to attain more accurate estimates and predictions of geopressure fields. A reliable pore pressure model clearly impacts on safety and costs issues related to drilling operations. Geostatistics is a branch of Statistics that develops and applies models representing natural phenomena whose proprieties vary according to its spatial location and could not be explained by deterministic functions. Its primary objective is to estimate the values and the prediction uncertainty of a sampled variable over an area of interest. Its main tool is the variogram, a function directly extracted from the sampled data that describes the spatial structure of the phenomenon. This results in an image of the phenomenon that honors sampled data and provides an estimate uncertainty map associated with the model. During oil exploration and exploitation operations, the acquisition of direct or primary data, such as well data, is scarce due to the elevated costs, which makes the estimates of the numeric model and the characterization of the reservoir less realistic. Thus, to increase the accuracy of the final models, indirect or secondary data such as sampled seismic data are used, which results in a better pore pressure model.

In this study we tested two multivariate methods (LVM (locally varying mean) kriging and collocated cokriging) in order to estimate the distribution of geopressures in a marine basin at depth levels relevant for exploration. These tests take into account pore pressure-related information derived from seismic velocity data. This integration results in a more consistent pore pressure model. Multivariate geostatistical techniques are promising tools for generation of high quality maps of pore pressure distribution and are fast, robust and easy to implement. In short, the generation of the geostatistical models presented in this study consists in four main stages: (1) Data preparation: this stage must be planned and executed by the interpreter. During the modeling of an interval, seismic attributes must correlate with the geological property under investigation; (2) Statistical exploratory analysis: primary data are evaluated using descriptive statistics and graph analysis, as frequency histograms and crossplot dispersion graphics, to evaluate the dependence of the available set of variables and spatial data distribution. (3) Variography: the study of spatial continuity and dependence by directional variogram modeling and analysis. (4) Estimate model: application of cokriging algorithms, resulting in an image with minimal variance. In this paper, we present a case study of an area on the equatorial margin of Brazil. Pore pressure gradients from five wells were used as the primary variable. This dataset is a compilation of information from formation tests, mud weight logs, pore pressure estimations from drilling parameters, leak-off tests and unexpected occurrences of kicks. As a secondary variable, a 3D cube of seismic interval velocity was used. The exploratory analysis demonstrated that the predictive and secondary variables are satisfactorily correlated, allowing to perform LVM and collocated cokriging procedures. Comparing the resulting maps, LVM estimate showed the most reliable interpolation, presenting more detailed and realistic maps with better resolution. In both cases, the resulting map showed high pressure throughout the interval of interest. This interval corresponds to a clayey section from the Upper Cretaceous with anomalous pore pressure fields. This study demonstrated the feasibility of the application of multivariate geostatistical technique to establish a numerical 3D representation of a relevant and potentially hazardous exploration and exploitation variable (pore pressure distribution) using ordinarily available data for prediction and quantification purposes.