# A Recovery Curve Based Method for Calculation of the Matrix-Fracture Mass Transfer in Naturally Fractured Petroleum Reservoirs

Christoph Steiner

Research output: ThesisDoctoral Thesis

## Abstract

This dissertations presents a method for the calculation of the matrix-fracture mass transfer in naturally fractured petroleum reservoirs based on the recovery curve concept, which was first introduced by Heinemann in 2004. This work extends previous efforts of research and development of Prof. Heinemann’s research group by successfully defining practically usable techniques for scaling recovery curves and thereby improving the recovery curve method. Clear evidence for the correctness of this method is presented in this dissertation. The applicability of other transfer models is also assessed and demonstrated utilizing numerical experiments. In 1960 Barenblatt, Zheltov and Kochina introduced the dual continuum concept and applied it to fractured reservoirs. In this concept a transfer term describes the interaction between the matrix and the fracture continuum. One of the most used and accepted methods for defining this transfer term is the transfer function introduced by Kazemi et al. in 1976. Using fine grid single matrix block calculations, the applicability of this type of transfer equation using shape factors is tested. It is evident that it is applicable in certain cases like single phase expansion, but not generally. Other concepts like Multiple Interacting Continua or Discrete Fracture Networks have been developed, but do not have industrial significance and are therefore not part of the investigations. Following the principle of the recovery curve concept, numerically derived recovery curves are directly utilized for determining the matrix-fracture mass transfer, instead of matching fitting parameters of equations to the results of single matrix block calculation. It is proved that it is possible to utilize a single recovery curve, calculated at bubble point pressure, for all possible matrix pressure and saturation conditions by scaling it. The therefore required scaling consists of two parts, one for the recovery factor increment and the other for the ultimate oil recovery of the single matrix block. The significance of the presented scaling method is demonstrated on both small and large scale models. It is shown that for accurate and reliable results both scaling of the recovery curve increment as well as the ultimate recovery is necessary.
Translated title of the contribution Eine auf Entölungskurven Basierende Methode zur Berechnung des Matrix-Kluft Massentransfers in Natürlich Geklüfteten Erdöllagerstätten English Dr.mont. Montanuniversität Heinemann, Zoltan, Assessor A (internal)Hofstätter, Herbert, Assessor B (internal) Published - 2018

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## Keywords

• Naturally Fractured Reservoirs
• Reservoir Simulation
• Dual Continuum Models
• Recovery Curve Method