Integrated Lithofacies and Petrophysical Properties Simulation
Authors: Bahar Asnul , Kelkar Mohan 
Published: December 2007

Abstract
This paper presents a new procedure that simultaneously generates consistent distributions of categorical lithofacies and continuous petrophysical properties, i.e., porosity and permeability. The technique used is the conditional simulation method which is capable of honoring the original distribution of the data and the associated spatial relationship. The simulation of lithofacies is conducted using the combination of indicator simulation and truncated Gaussian simulation techniques whereas the porosity simulation is conducted using the sequential Gaussian simulation. To generate the permeability simulation, the conditional distribution technique is used.
Previously, to generate petrophysical properties consistent with geological description, investigators have used two step approach where geological description are constructed first, and the petrophysical properties are described in the next step through a filtering process. In contrast, in the approach used in this paper, each grid block is visited only once. Using the same search neighborhood, the geological facies is estimated first, followed by porosity and permeability values. The method accounts for correlations among these variables as well as the spatial relationships. This reduces the storage requirements and makes the process computationally efficient.
The method was successfully validated using the field data. Both sandstone and carbonate fields were used to generate the facies/rock type, porosity, and permeability distributions. The simulated geological descriptions matched well with the geologists' interpretation. Further the results were consistent with the observed production performance in terms of quality of rocks and petrophysical properties.
The implementation of this new procedure is done using the C++ language. The implementation includes the user interface program which operates in Windows 95 / NT system. Using this program, the user is able to perform variogram analysis, to prepare the required parameter file, to run the simulation, and to view the graphical results, i.e., the cross sections, directly from the screen.

Introduction
Reservoir characterization is the process of generating reservoir properties, mainly porosity and permeability, by integrating many types of data. An objective of performing reservoir characterization is to better predict the future performance of the reservoir. A tool that can be used to perform reservoir characterization is geostatistics. Various geostatistical techniques have been developed in the industry to perform this task. Some of the most important techniques are conditional simulation techniques which include sequential Gaussian simulation, sequential indicator simulation, truncated Gaussian simulation and probability field simulation.
A common practice in the industry in developing reservoir properties with a consistent underlying geological description is to apply the two-stage approach. In the first stage, the geological description is simulated using a conditional simulation technique such as sequential indicator simulation or Gaussian truncated simulation to produce the detailed geological simulation. In the second stage, petrophysical properties are simulated for each type of the geological facies/unit using a conditional simulation technique such as sequential Gaussian simulation or simulated annealing. The simulated petrophysical properties are then filtered using the generated geological simulation to produce the final description. The main problem of this approach is efficiency, since it requires intensive computation time.
The effort to jointly simulate interdependent random variables has been discussed by several authors. The techniques used by these authors have produced reasonable results. Common disadvantages of these technique are the requirement of tedious inference and modeling of covariances and cross covariances. Also large cpu-time to solve the numerical solution of a large cokriging system is required.
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