Pressure Transient Analysis for Naturally Fractured Reservoirs

Abstract

New ideas are presented for the interpretation of pressure transient tests for wells in naturally fractured reservoirs. This work is based on the transient matrix flow model formulated by de Swaan. The differences between this model and the Warren and Root model occur during the transition flow period. It is demonstrated that the behavior of a naturally fractured reservoir can be correlated by using three dimensionless parameters. (i.e.). It is established that regardless of matrix geometry the transition period might exhibit a straight line whose slope is equal to half the slope of the classical parallel semilog straight lines, provided the transient matrix linear flow is present. In addition, information is provided on the estimation of fracture area per unit matrix volume or matrix parameters from the transition period semilog straight line. it is shown, that matrix geometry might be identified when pressure data are smooth. Field examples are included to illustrate the application and the validity of the theoretical results of this study. Introduction One of the rock heterogeneities that has deserved the attention of many investigators is the presence of fractures crossing the producing formations. Many of the important producing fields around the world are found in fractured formations in spite of this, during the last decades most of the reservoir engineering studies have been oriented towards homogeneous systems. It appears that the first study on the performance of a fractured reservoir was published in 1932. Regarding pressure transient analysis on fractured formations, commonly called naturally fractured, a review of the literature shows that it was initially discussed by Pollard. He was interested on the determination of fracture volume from pressure build up tests. His method was advanced by Pirson and Pirson' to include a calculation method for the matrix volume of a fractured reservoir. The first to present a detailed discussion of the radial flow of a slightly compressible fluid through a naturally fractured reservoir were Barenblatt and Zheltov and Barenblatt et al. (Fig 1). These authors assume that the flow occurs only in the fracture medium and that the matrix blocks are a source that delivers flow to the fracture system and that this flow could be considered under pseudosteady-state flow conditions.

Pressure-Transient Behavior of DoublePorosity Reservoirs with Transient Interporosity Transfer with Fractal Matrix Blocks

“…The fluid transfer function for infinite-acting matrix blocks is: Asymptotic Behavior. As pointed out by Cinco-Ley et al (1982), the flow from the matrix blocks to the fracture network is linear at early and intermediate times (Periods 1 and 2) regardless the geometry of the matrix block. During these periods of flow, the behavior of the fluid transfer function for closed and infinite-acting matrix blocks are the same.…”

“…Double-porosity Model considering a radial fracture Network and Fractal Matrix Blocks To model the flow within the radial fracture network, we have considered the diffusivity equation presented by Cinco-Ley et al (1982). In its dimensionless form, this result is given by:…”

“…5), the model given by Eq. 15 can be simplified to yield: (17) where: 18A similar model for radial fracture networks and Euclidean matrix blocks was developed by Cinco-Ley et al (1982). By analogy, for late times, substituting Eq.…”

“…Eq. 19 has the same shape as the models assuming the anomalous diffusion phenomena (Camacho-Velazquez et al, 2008 andRaghavan, 2012), but this model takes into account physical properties related to the geology of the the matrix blocks. The asymptotic constant-rate solutions in the real domain of Eq.…”

“…The periods of flow exhibited by the dual porosity model with transient interporosity transfer conditions are (see Fig. 1): In 1982, three independent research groups (i.e., Cinco-Ley et al, Serra et al, and Streltsova) modified de Swaan's model and obtained asymptotic solutions in the real domain -in this work, we use the model presented by Cinco-Ley et al (1982). Traditionally, fractal diffusivity models have been used to model highly heterogenous reservoirs (e.g., NFRs and shale reservoirs).…”