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Conditional simulation is a geostatistical approach to generate multiple equiprobable distributions of a property with specified univariate and spatial attributes. These attributes are derived from sample data or inferred from external information. This paper evaluates the effectiveness of conditional simulation to describe distributions of porosity in a carbonate environment. The reservoir studied produces from a dolomitized formation of complex lithology. The conditional simulation methods tested are the simulated annealing simulation (SAS) and the sequential indicator simulation (SIS). A validation procedure is introduced to compare observed and simulated procedure is introduced to compare observed and simulated porosity distributions and to quantify the quality of porosity distributions and to quantify the quality of two- and three-dimensional conditional simulations. Results of three- dimensional validations indicate that SAS yields a good overall reproduction of observed porosity distributions. Comparisons of equiprobable two-dimensional distributions suggest that the quality of the porosity descriptions for SAS are slightly better than for SIS. These results show that conditional simulation renders descriptions which capture variations of a property due to inherent geologic complexities. The major advantages of conditional simulation over traditional methods are:

  1. it incorporates in a distribution of a property different degrees of variability for different directions, and

  2. it accounts for uncertainties in the description.

Introduction

Spatial distributions of reservoir properties, in particular, porosity and permeability, play an important role in porosity and permeability, play an important role in predictions of hydrocarbon reserves and fluid flow performance. predictions of hydrocarbon reserves and fluid flow performance. Logs and cores of vertical and horizontal wells, geologic models and outcrop observations and seismic data provide evidence of the irregular distribution of reservoir properties. Depending on factors such as depositional environment, the nature of the distribution of a property is often characterized by spatial variability which is manifested as anisotropy with different degrees of variation along different directions for different scales. Despite this complex nature of properties, the traditional approach has been to represent distributions by oversimplified models (e.g., layer cake models of constant properties). In many cases, such as the carbonate reservoir properties). In many cases, such as the carbonate reservoir considered in this paper, a layer cake model is not consistent with geologic conceptions of the environment. As an alternative to these simplistic and often subjective models, this paper investigates the robustness of conditional simulation methods to describe the complex variability of reservoir properties. properties. Conditional simulation can be defined as a methodology to generate equi-probable distributions of a property constrained by:

  1. conditioning data and

  2. a set of statistical parameters.

Conditioning data consist of sample data of a parameters. Conditioning data consist of sample data of a property observed at wells, such as porosity or permeability property observed at wells, such as porosity or permeability derived from logs or cores.

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