Innovative Data-Driven Permeability Prediction in a Heterogeneous Reservoir

Abstract

Abstract In complex reservoirs where heterogeneity of properties and errors associated with sampling yield uncertain measurements of geological properties, e.g. porosity and permeability, conventional techniques such as empirical and nonlinear regression methods attempt to estimate values of these properties with low or no error. Conversely, artificial intelligence asserts that the error contains useful information that complements conventional techniques. For example, fuzzy logic methods to predict permeability at uncored wells provide uncertainty measures based on secondary variables such gamma ray, neutron porosity, sonic porosity, bulk density, formation resistivity, and core-based permeability. Fuzzy logic provides tools for uncertainty modeling and improved permeability estimation. Here, a two-stage fuzzy ranking algorithm is integrated in the fuzzy predictive model to improve generalization capability and transparency of the model through selecting inputs best suited to predict permeability. Fuzzy curve and surface analysis is used to rapidly and automatically identify information-rich well logs and filter out data dependencies. Subtractive clustering algorithm generates membership functions and isolates clusters of data. The Takagi-Sugeno-Kang fuzzy rule-based system (TSK) is constructed from a subset of logs and core measurements. The antecedent fuzzy sets are obtained by projecting the mean and variance onto input data axes. The consequent functions consist of a set of linear equations. To tune antecedent and consequent membership function parameters, an Adaptive Network based fuzzy inference systems (ANFIS) is used. The proposed methodology is initially validates using the standard Box & Jenkins' gas furnace data to predict CO2 concentration and compared to a multilinear regression technique. Generalization capability has increased through using the most significant inputs during modeling gas furnace data. The methodology was also demonstrated by predicting permeability from well log data of a heterogeneous sandstone reservoir located in the Middle East. The fuzzy model was compared to conventional linear and multilinear regression models to show its applicability and superiority in heterogeneous systems. Unlike conventional methods, the proposed fuzzy technique does not require any prior knowledge of the reservoir and relationships between permeability and input variables. In addition, the technique accounts for uncertainty that exists in log data. The result is an efficient interpretation expert system that can be continuously conditioned as new data becomes available. Introduction In reservoir engineering, it is of great importance to characterize how the lithology and geology of the rocks are related to the well logs such as porosity, density and gamma ray. Permeability is the key variables in characterizing a reservoir and in determining flow patterns in order to optimize the production of a field. However, this type of reservoir characterization is under uncertainty, precarious correlations between rock parameters and data sets that are suffering natural and human perturbing effects. Well log data are often difficult to analyze because of their complexity, lack of conventional methods to account for uncertainty associated with vagueness, impression and/or lack of information, and limited human ability to understand and use the information content of these data. Permeability is recognized as a complex function of several interrelated factors such as lithology, pore-fluid composition and porosity. Thus, permeability estimates from well logs often rely upon porosity, e.g. through the Kozeny-Carman equation, which also contains adjustable factors such as the Kozeny constant, which varies within the range 5±100 depending on the reservoir rock and grain geometry (Rose and Bruce 1949).