Application of Fractal Reservoir Model for Interference Test Analysis in Kamojang Geothermal Field (Indonesia)

Abstract

Abstract This paper presents the application of a new concept, i.e.; fractal model, to analyze pressure transient test data in complex naturally fractured geothermal reservoir. Application of conventional type curves has been unsuccessful in analyzing and interpreting the interference test results in Kamojang geothermal reservoir which is considered as a complex naturally fractured system. Using the conventional type curve method, the pressure test data, in this case, cannot match to the curve, primarily at early time data. The match, however, can be achieved by using the type curves generated based on "fractal reservoir model" which has been previously developed by Chang and Yortsos in 1990. Using the diffusivity equation of fractal reservoir, the equation for interference test has been derived and the result is then used for generating a new type curve method. In addition, the procedure to use this method has also been developed. Using the generated type curves, application has been performed on analyzing the interference test data from Kamojang geothermal reservoir. The analyzing results demonstrate the viability of the model in describing characteristics of the reservoir such as transmissibility, storativity and fractal dimension of the medium. Introduction Previous work showed that the fractal reservoir model could be used satisfactorily in describing the pressure transient behavior in the reservoir. In their model, the fracture network is assumed to be connected and distributed as a fractal object within a homogeneous medium (matrix) of Euclidean geometry. Fluid flow from reservoir to wells, in such a reservoir, occurs only through the perfectly connected fracture network. Based on these approaches, they used diffusivity equation to model a transient flow in the fractal reservoir for single well problems. In this paper, the application of fractal reservoir model for handling the multiple well problems, especially in analyzing the interference test data, is discussed. Physical and mathematical descriptions of this model are basically adopted from the model that had been developed by Chang and Yortsos (1990). By involving several mathematical manipulations into the model, the formulation can be extended and used for multiwell test problems. Then, using this equation, type curve model for interference test analysis can be generated by plotting two variable groups which have been defined in this study. The interference test data in Kamojang geothermal reservoir which is considered as a complex naturally fractured reservoir has been analyzed to determine transmissibility, storativity and fractal dimension of the reservoir. DEVELOPMENT OF THE PROPOSED MODEL The fractal model is able to appropriately described the complex naturally fractured reservoir which has a large number of different scale, poor fracture connectivity and disorder spatial distribution. In the pressure transient case, the application of fractal model has been examined by Acuna et al. for analyzing single well test data in naturally fractured reservoir of geothermal field. Using their model, the method that could be used in the Interference Test Analysis was developed. By considering at least two interference wells in a fractal reservoir, one of them is an active well and the others are observation wells (see Figure 1), a pressure transient equation has been formulated in this study. Using this equation, a procedure of type curve matching is then proposed for analyzing some reservoir parameters, such as reservoir transmissibility, storativity and fractal dimension. P. 511^