Geostatistical Modeling of Permeability With Annealing Cosimulation (ACS)

To provide accurate predictions of flow performance, the numerical model of permeability used by flow simulators must be consistent with all available geological and engineering data. The available data includes core permeability measurements, relevant permeability statistics (particularly, histograms, measures of spatial variability, and correlation with secondary variables such as porosity), and well test-derived permeability measurements. This paper documents an algorithm to generate 3-D permeability models that honor this variety of data. The =-.... algorithm, referred to as annealing cosimhlation (ACS), generates stochastic permeability models using the numerical optimization algorithm known as simulated annealing. The .-nl;fi.f;fin nf cimulatwl annealinp tn re~erv~i~ modeling is not @HJJJ--L~~~J u. . .... .. .. . ~....--..... a -_ new. The variety of information considered, however, and the practical example presented in this paper will be of interest to reservoir modelers. Introduction Geostatistical techniques are increasingly being used to generate the 3-D numerical models of rosity and permeability required for reservoir simulation. 1‘2*P The quality of a geostatistical model is directly related to how well it honors the available geological and engineering data. This paper documents the application of simulated annealing to the generation of 3-D permeability models. The originality of this paper is in the details of application that allow the practical and simultaneous integration of many sources of data. One promise of geostatistics is a range of equiprobable models that may be used to quantify the uncertainty in the reservoir model. At times, there appears to be a wealth of data (core, well logs, seismic, production tests, and so on). Even in these ideal situations, however, the data are inadequate to provide a unique reservoir model; there is always uncertainty in the assignment of reservoir properties at unsampled locations. To account for important geological variations, porosity and permeability must be modeled within homogeneous “rock types” that art= h~ct=dQH~ ~~~i~na]!i~holq#facies model constructed .l, La. -w “-within a detailed sequence (or chrono-) stratigraphic framework.4 There is a place for stochastic techniques in the construction of rock type models and stratigraphic frameworks, 1--------A-.-..-..:-:.+:,:..l*a9-nra*; ,rwmcrhwtac rlnminnte ~~~S nuwmb, UGLCi Illllllsuu mmpu.lk pw”””l”. . . . . . . . . . . aspect of reservoir description. Uncertainty in the stratigraphic framework and geological concept are difficult to quantify. In many cases, however, these aspects of uncertain y are the most consequential. This is one reason why the integration of all available information is considered more important than the generation of multiple realizations and the subsequent quantification of uncertainty. As stated above, porosity and permeability must be modeled within homogeneous rock types. The modeling, however, can not be performed independently within each rock type. Firstly, there may be spatial correlation in the porosity and permeability across rock type boundaries. Secondly, engineering-type data (production history, surveillance, and well test measurements) and geophysical-type data (seismic attributes) inform volumes