Generation of Porosity and Permeability Fields Conditioned to Geostatistical and Pressure Transient Data

Abstract

AbstractThis study aims at the generation of permeability and porosity distributions conditioned to geostatistical (variogram, mean values of permeability and porosity), static (well-logging, core etc.) and well-test pressure data and the assessment of uncertainty in generated distribution and performance prediction. Integration of all the available data from different sources (static, well test, geostatistical, etc.) into reservoir description is prerequisite for reliable performance predictions. It is shown that reservoir characterization solely based on geostatistical, static or well test pressure data imposes a nonunique problem to be solved. Specifically, by using 1-D and 2-D numerical flow simulators, we show that the pressure transient response obtained at a single well cannot provide unique determination of permeability. This necessitates the direct incorporation of well test pressure data as well as geostatistical and static data into reservoir description to resolve porosity and permeability distributions in lateral (or inter-well) directions. It is shown that the inverse problem theory based on Bayesian statistics provides a powerful methodology to incorporate different sources of data into reservoir characterization. Moreover, it provides means to assess the uncertainty in reservoir description generated and performance predictions based on such descriptions. By assuming multinormal distributions for porosity and log-permeability fields, an application of Bayesian estimation methodology to reservoir characterization is presented.