Abstract

The use of fractal model in Pressure Transient Test Analysis was introduced by Chang and Yortsos in 1990. Their concept was derived from the assumption of Warren and Root model where their reservoir contains two systems with contrast in porosity and pemeability properties, which are well-known as matrix and fracture network.

The fracture network is assumed to be connected and distributed as fractal object in a homogeneous medium (matrices) of Euclidean Geometry. Fluid flow from reservoir to well occurs only through the perfectly connected fracture network. Based on these assumptions, Chang and Yortsos developed the unsteady-state flow of slightly compressible fluid and proposed an extension of the diffusivity equation to model transient flow in fractured reservoirs, especially in single well testing.

The physical and mathematical model descriptions are developed from Chang and Yortsos model. By Type Curve Matching technique, we can analyze the interference test in reservoir considered as a complex naturally fractured reservoir such as the one operated by Amoseas Indonesia Inc. Besides transmissibility and storativity we can also obtain the fractal dimension which can be used to predict the complexity of the reservoir.

Introduction

In 1982, Mandelbrot B.B., introduced the concept of fractal geometry that is a relatively new approach for describing and modeling of complex objects and processes. In Petroleum Engineering these concepts are then used for characterizing fractal behavior of porous media and analyzing pressure gradient of fractal objects. Fractal geometry provides a method to account for a great variety of such transients under the assumption that the network behaves as fractal objects.

The application of fractal model or concepts to pressure transient testing in fractal fractured system was proposed by Chang and Yortsos, who described the diffusivity equation to transient flow model in fractal reservoir for single well problems. The fractal model is able to appropriately describe a complex naturally fractured reservoir which has a large number of different scale, poor fracture connectivity and disorderly spatial distribution. In the pressure transient case, the application of fractal model has been examined by Acuna et. al., (Ref. 2), for analyzing single well test data in naturally fractured reservoirs. Using their model, a method that could be used in an interference test analysis was developed. By considering at least two interfering wells in a fractal reservoir, one of them being an active well and the others are observation wells, a pressure transient equation was formulated by Abdassah, D., and Aprilian, S. (Ref. 8).

In this paper, development and practical application of new type curves using fractal concept for handling the multiple well test problems, especially in analyzing the interference test, are discussed. The objective of this study is to obtain reservoir characteristics such as permeability thickness, storativity, transmissibility and fractal dimension of the Darajat Field, Amoseas Indonesia, Inc., (Fig. 1), by applying the new type curve in interference test.

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